Tel Aviv Topology Conference: Rothenberg Festschrift
Author:
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 320
ISBN-13: 9780821855676
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Tel Aviv Topology Conference: Rothenberg Festschrift
Author: Melvin Rothenberg
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 334
ISBN-13: 0821813625
DOWNLOAD EBOOK →This volume presents the proceedings of the Tel Aviv International Topology Conference held during the Special Topology Program at Tel Aviv University. The book is dedicated to Professor Mel Rothenberg on the occasion of his 65th birthday. His contributions to topology are well known-from the early work on triangulations to numerous papers on transformation groups and on geometric and analytic aspects of torsion theory. Current research related to those contributions are reported in this book. Coverage is included on the following topics: vanishing theorems for the Dirac operator, the theory of Reidemeister torsion (including infinite dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of group actions, Lusternik-Schnirelman theory for closed 1-forms, finite type invariants of links and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and more.
Tel Aviv Topology Conference, Rothenberg Festschrift
Tel Aviv Topology Conference, Rothenberg Festschrift
L2-Invariants: Theory and Applications to Geometry and K-Theory
Author: Wolfgang Lück
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 604
ISBN-13: 3662046873
DOWNLOAD EBOOK →In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
Homotopy Methods in Algebraic Topology
Author: Nicholas Kuhn
Publisher: American Mathematical Soc.
Published: 2001-04-25
Total Pages: 370
ISBN-13: 0821826212
DOWNLOAD EBOOK →This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.
Introduction to Symplectic Dirac Operators
Author: Katharina Habermann
Publisher: Springer
Published: 2006-10-28
Total Pages: 131
ISBN-13: 3540334211
DOWNLOAD EBOOK →This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
Asymptotic Formulae in Spectral Geometry
Author: Peter B. Gilkey
Publisher: CRC Press
Published: 2003-12-17
Total Pages: 312
ISBN-13: 0203490460
DOWNLOAD EBOOK →A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computi
Low Dimensional Topology
Author: Hanna Nencka
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 266
ISBN-13: 0821808842
DOWNLOAD EBOOK →"The book has two main parts. The first is devoted to the Poincare conjecture, characterizations of PL-manifolds, covering quadratic forms of links and to categories in low dimensional topology that appear in connection with conformal and quantum field theory.
Parametrized Homotopy Theory
Author: J. Peter May
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 456
ISBN-13: 0821839225
DOWNLOAD EBOOK →This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.
