Semistability Of Amalgamated Products And Hnn Extensions

Author : Michael L. Mihalik,Steven Thomas Tschantz
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 54,5 Mb
Release : 1992
Category : Free products
ISBN : 9780821825310

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Semistability of Amalgamated Products and HNN-Extensions by Michael L. Mihalik,Steven Thomas Tschantz Pdf

In this work, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work.

Author : Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary
Publisher : Springer
Page : 174 pages
File Size : 43,7 Mb
Release : 2016-09-14
Category : Mathematics
ISBN : 9783319436746

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Topology and Geometric Group Theory by Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary Pdf

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 45,7 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780387746142

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Topological Methods in Group Theory by Ross Geoghegan Pdf

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Author : Jean-Pierre Gabardo
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 55,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825518

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Extension of Positive-Definite Distributions and Maximum Entropy by Jean-Pierre Gabardo Pdf

In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.

Author : André Joyal,Myles Tierney
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 46,6 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821823125

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An Extension of the Galois Theory of Grothendieck by André Joyal,Myles Tierney Pdf

Author : Cristiano Husu
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 52,7 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825716

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Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules by Cristiano Husu Pdf

This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative ${\mathbf Z}_2$-twisted vertex operators are then introduced, and a Jacobi identity for these operators is established. Husu uses these ideas to interpret and recover the twisted Z -operators and corresponding generating function identities developed by Lepowsky and Wilson for the construction of the standard $A^{(1)}_1$-modules. The point of view of the Jacobi identity also shows the equivalence between these twisted Z-operator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The Lepowsky-Wilson generating function identities correspond to the identities involved in the construction of a basis for the space of C-disorder fields of such parafermion algebras.

Author : Percy Deift,Luen-Chau Li,Carlos Tomei
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 40,9 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825402

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Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions by Percy Deift,Luen-Chau Li,Carlos Tomei Pdf

The theory of classical $R$-matrices provides a unified approach to the understanding of most, if not all, known integrable systems. This work, which is suitable as a graduate textbook in the modern theory of integrable systems, presents an exposition of $R$-matrix theory by means of examples, some old, some new. In particular, the authors construct continuous versions of a variety of discrete systems of the type introduced recently by Moser and Vesclov. In the framework the authors establish, these discrete systems appear as time-one maps of integrable Hamiltonian flows on co-adjoint orbits of appropriate loop groups, which are in turn constructed from more primitive loop groups by means of classical $R$-matrix theory. Examples include the discrete Euler-Arnold top and the billiard ball problem in an elliptical region in $n$ dimensions. Earlier results of Moser on rank 2 extensions of a fixed matrix can be incorporated into this framework, which implies in particular that many well-known integrable systems--such as the Neumann system, periodic Toda, geodesic flow on an ellipsoid, etc.--can also be analyzed by this method.

Author : Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 46,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825617

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Continuous Images of Arcs and Inverse Limit Methods by Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn Pdf

Continuous images of ordered continua have been studied intensively since 1960, when S. Mardsic showed that the classical Hahn-Mazurkiewicz theorem does not generalize in the ``natural'' way to the nonmetric case. In 1986, Nikiel characterized acyclic images of arcs as continua which can be approximated from within by a sequence of well-placed subsets which he called T-sets. That characterization has been used to answer a host of outstanding questions in the area. In this book, Nikiel, Tymchatyn, and Tuncali study images of arcs using T-set approximations and inverse limits with monotone bonding maps. A number of important theorems on Peano continua are extended to images of arcs. Some of the results presented here are new even in the metric case.

Author : Stanley O. Kochman
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 55,7 Mb
Release : 1993
Category : Adams spectral sequences
ISBN : 9780821825587

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Symplectic Cobordism and the Computation of Stable Stems by Stanley O. Kochman Pdf

This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.

Author : J. F. Jardine
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 46,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825907

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Higher Spinor Classes by J. F. Jardine Pdf

This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Frohlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-Witt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 etale cohomology.

Author : Oscar Zariski
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 50,7 Mb
Release : 1951
Category : Algebraic functions
ISBN : 9780821812051

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Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields by Oscar Zariski Pdf

Author : David Soudry
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 43,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825686

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Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory by David Soudry Pdf

This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $21n$ of generic representations of $\textnormal{SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$. The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and $L$-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor ($1

Author : F. Thomas Farrell,Lowell Jones
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 53,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825532

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Markov Cell Structures near a Hyperbolic Set by F. Thomas Farrell,Lowell Jones Pdf

The authors' argument is a spiritual descendent of earlier work of Adler and Weiss, Sinaĭ, and Bowen, and involves a close study of triangulations. The discussion is long and technical, but the outline of the proof is sketched clearly in Section 1 for the special case of [italic]F an expanding immersion. A concluding section lists problems on hyperbolic sets, Markov partitions, and related matters; remarks on topological invariants, including the conjectured vanishing of Pontryagin classes for manifolds supporting Anosov diffeomorphisms, may be of particular interest.

Author : Shirō Gotō,Koji Nishida
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 43,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825846

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The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations by Shirō Gotō,Koji Nishida Pdf

This monograph consists of two parts. Part I investigates the Cohen-Macaulay and Gorenstein properties of symbolic Rees algebras for one-dimensional prime ideals in Cohen-Macaulay local rings. Practical criteria for these algebras to be Cohen-Macaulay and Gorenstein rings are described in terms of certain elements in the prime ideals. This framework is generalized in Part II to Rees algebras $R(F)$ and graded rings $G(F)$ associated to general filtrations of ideals in arbitrary Noetherian local rings. Goto and Nishida give certain cohomological characterizations for algebras $R(F)$ to be Cohen-Macaulay or Gorenstein rings in connection with the corresponding ring-theoretic properties of $G(F)$. In this way, readers follow a history of the development of the ring theory of Rees algebras. The book raises many important open questions.

Author : Melvin Hochster,Craig Huneke
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 50,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825563

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Phantom Homology by Melvin Hochster,Craig Huneke Pdf

This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic $p$. The book would be suitable for use in an advanced graduate course in commutative algebra.