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 Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems.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.

Surveys on Surgery Theory

Author: Sylvain F. Cappell
Publisher: Annals of Mathematics Studies
ISBN: 0691049386
Release Date: 2000
Genre: Mathematics

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

Third International Congress of Chinese Mathematicians

Author: Ka-Sing Lau
Publisher: Amer Mathematical Society
ISBN: UOM:39015075618416
Release Date: 2008
Genre: Mathematics

This volume consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics.