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Author : Anonim
Publisher : Academic Press
Page : 316 pages
File Size : 51,5 Mb
Release : 1986-12-22
Category : Mathematics
ISBN : 0080874436
Decompositions of Manifolds
Author : Robert J. Daverman
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 48,7 Mb
Release : 2007
Category : Mathematics
ISBN : 0821843729
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to everyone who is interested in this subject. The book also contains an extensive bibliography and a useful index of key words, so it can also serve as a reference to a specialist.
Author : R. H. Bing,William T. Eaton,Michael Starbird
Publisher : Unknown
Page : 288 pages
File Size : 46,5 Mb
Release : 1983-07
Category : Mathematics
ISBN : UCAL:B4406909
Author : Danny Calegari
Publisher : Clarendon Press
Page : 384 pages
File Size : 48,7 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780191524639
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author : Steve Armentrout
Publisher : American Mathematical Soc.
Page : 76 pages
File Size : 46,7 Mb
Release : 1971
Category : Decomposition (Mathematics)
ISBN : 9780821818077
Author : Krzysztof P. Wojciechowski
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 45,7 Mb
Release : 2005
Category : Algèbres d'opérateurs - Congrès
ISBN : 9780821835364
In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general theory of spectral invariants on closed manifolds and manifolds with boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as traces, indices, and determinants. Part III is concerned with general geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Author : Günter Schwarz
Publisher : Springer
Page : 161 pages
File Size : 45,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540494034
Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.
Author : Jan de Gier,Cheryl E. Praeger,Terence Tao
Publisher : Springer Nature
Page : 803 pages
File Size : 48,5 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9783030624972
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Author : Andrew Ranicki
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 45,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662120118
Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
Author : R. H. Crowell,R. H. Fox
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299356
Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.
Author : Hansjörg Geiges
Publisher : Cambridge University Press
Page : 8 pages
File Size : 50,7 Mb
Release : 2008-03-13
Category : Mathematics
ISBN : 9781139467957
This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
Author : John Harer,Arnold Kas,Robion C. Kirby
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 43,8 Mb
Release : 1986
Category : Geometry, Algebraic
ISBN : 9780821823514
This monograph gives framed link pictures of the Kummer surface (= [italic]V4) and some Dolgachev surfaces. The emphasis here is to use the elliptic pencil structure to describe the framed links. This approach is particularly convenient to see the change of handlebody structures of elliptic surfaces after an operation of logarithmic transform, which is an important ingredient in constructing Dolgachev surfaces.
Author : Suhyoung Choi
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 41,6 Mb
Release : 2001
Category : Three-manifolds
ISBN : 9780821827048
An affine manifold is a manifold with torsion-free flat affine connection - a geometric topologist would define it as a manifold with an atlas of charts to the affine space with affine transition functions. This title is an in-depth examination of the decomposition and classification of radiant affine 3-manifolds - affine manifolds of the type that have a holonomy group consisting of affine transformations fixing a common fixed point.
Author : Frederick Carter Tinsley
Publisher : Unknown
Page : 356 pages
File Size : 42,8 Mb
Release : 1977
Category : Manifolds (Mathematics)
ISBN : WISC:89010952570
Author : Jennifer Schultens
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 44,6 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9781470410209
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.