Algebraic L theory and Topological Manifolds

Author: A. A. Ranicki
Publisher: Cambridge University Press
ISBN: 0521420245
Release Date: 1992-12-10
Genre: Mathematics

Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

Automorphisms of Manifolds and Algebraic K Theory Part III

Author: Michael S. Weiss
Publisher: American Mathematical Soc.
ISBN: 9781470409814
Release Date: 2014-08-12
Genre: Mathematics

The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.

High dimensional Knot Theory

Author: Andrew Ranicki
Publisher: Springer Science & Business Media
ISBN: 9783662120118
Release Date: 2013-04-17
Genre: Mathematics

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.

Handbook of K Theory

Author: Eric Friedlander
Publisher: Springer Science & Business Media
ISBN: 9783540230199
Release Date: 2005-07-18
Genre: Mathematics

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Ends of Complexes

Author: Bruce Hughes
Publisher: Cambridge University Press
ISBN: 0521576253
Release Date: 1996-08-28
Genre: Mathematics

A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.

Dynamical Systems and Semisimple Groups

Author: Renato Feres
Publisher: Cambridge University Press
ISBN: 0521591627
Release Date: 1998-06-13
Genre: Mathematics

This book comprises a systematic, self-contained introduction to the Margulis-Zimmer theory and provides an entry into current research. Taking as prerequisites only the standard first-year graduate courses in mathematics, the author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts normally covered in first courses on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions, and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore's ergodicity theorem.

Surveys on Surgery Theory

Author: Sylvain Cappell
ISBN: 0691088152
Release Date: 2000
Genre: Mathematics

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.