Global Analysis On Foliated Spaces

Author : Calvin C. Moore,Claude Schochet
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461395928

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Global Analysis on Foliated Spaces by Calvin C. Moore,Claude Schochet Pdf

Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory.

Author : Philippe Tondeur
Publisher : Birkhäuser
Page : 308 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889148

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Geometry of Foliations by Philippe Tondeur Pdf

The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.

Author : Dominique Cerveau
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 55,6 Mb
Release : 2003
Category : Mathematics
ISBN : 082183228X

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Complex Dynamics and Geometry by Dominique Cerveau Pdf

In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.

Author : Tadayoshi Mizutani,Kazuo Masuda,Shigenori Matsumoto,Takashi Inaba,Takashi Tsuboi,Yoshihiko Mitsumatsu
Publisher : World Scientific
Page : 514 pages
File Size : 47,5 Mb
Release : 1994-12-16
Category : Electronic
ISBN : 9789814550390

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Geometric Study Of Foliations - Proceedings Of The International Symposium/workshop by Tadayoshi Mizutani,Kazuo Masuda,Shigenori Matsumoto,Takashi Inaba,Takashi Tsuboi,Yoshihiko Mitsumatsu Pdf

This book covers recent topics in various aspects of foliation theory and its relation with other areas including dynamical systems, C∗-algebras, index theory and low-dimensional topology. It contains survey articles by G Hector, S Hurder and P Molino, as well as more than 20 original papers by specialists who are currently most active in the field.

Author : Tadayoshi Mizutani
Publisher : World Scientific
Page : 514 pages
File Size : 54,7 Mb
Release : 1994
Category : Foliations (Mathematics)
ISBN : 9789814533836

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Proceedings of the International Symposium/Workshop on Geometric Study of Foliations by Tadayoshi Mizutani Pdf

Author : Pawel Walczak,Remi Langevin,Takashi Tsuboi,Steven Hurder
Publisher : World Scientific
Page : 490 pages
File Size : 43,8 Mb
Release : 2006-09-20
Category : Mathematics
ISBN : 9789814476782

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Foliations 2005 - Proceedings Of The International Conference by Pawel Walczak,Remi Langevin,Takashi Tsuboi,Steven Hurder Pdf

This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference.

Author : Jesús A. Álvarez López,Alberto Candel
Publisher : Springer
Page : 173 pages
File Size : 48,5 Mb
Release : 2018-07-28
Category : Mathematics
ISBN : 9783319941325

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Generic Coarse Geometry of Leaves by Jesús A. Álvarez López,Alberto Candel Pdf

This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.

Author : Shigeru Kanemitsu,Chaohua Jia
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 42,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475736755

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Number Theoretic Methods by Shigeru Kanemitsu,Chaohua Jia Pdf

This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.

Author : J. Szenthe
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401152761

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New Developments in Differential Geometry, Budapest 1996 by J. Szenthe Pdf

Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

Author : Vladimir Rovenski
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242703

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Foliations on Riemannian Manifolds and Submanifolds by Vladimir Rovenski Pdf

This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.

Author : Shmuel Weinberger
Publisher : Cambridge University Press
Page : 365 pages
File Size : 52,6 Mb
Release : 2022-11-30
Category : Mathematics
ISBN : 9781107142596

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Variations on a Theme of Borel by Shmuel Weinberger Pdf

Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Author : Marc Burger,Alessandra Iozzi
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662047439

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Rigidity in Dynamics and Geometry by Marc Burger,Alessandra Iozzi Pdf

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.

Author : William Hilal Kazez
Publisher : American Mathematical Soc.
Page : 622 pages
File Size : 40,8 Mb
Release : 1996-10-22
Category : Mathematics
ISBN : 0821806548

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Geometric topology by William Hilal Kazez Pdf

This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.

Author : Andrew J. Blumberg,Teena Gerhardt,Michael A. Hill
Publisher : Cambridge University Press
Page : 441 pages
File Size : 50,5 Mb
Release : 2022-07-21
Category : Mathematics
ISBN : 9781009123297

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Stable Categories and Structured Ring Spectra by Andrew J. Blumberg,Teena Gerhardt,Michael A. Hill Pdf

A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.

Author : Percy Deift,Peter Forrester
Publisher : Cambridge University Press
Page : 539 pages
File Size : 48,6 Mb
Release : 2014-12-15
Category : Language Arts & Disciplines
ISBN : 9781107079922

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Random Matrix Theory, Interacting Particle Systems and Integrable Systems by Percy Deift,Peter Forrester Pdf

This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.