Algebraic L-theory and Topological Manifolds

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Author: A. A. Ranicki

Publisher: Cambridge University Press

ISBN: 9780521420242

Category: Mathematics

Page: 358

View: 6200

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

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Author: Michael S. Weiss, Bruce E. Williams

Publisher: American Mathematical Soc.

ISBN: 147040981X

Category: Mathematics

Page: 110

View: 6142

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.

Lower K- and L-theory

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Author: Andrew Ranicki

Publisher: Cambridge University Press

ISBN: 9780521438018

Category: Mathematics

Page: 174

View: 8459

This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Oberwolfach 1993

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Author: Steven C. Ferry

Publisher: Cambridge University Press

ISBN: 9780521497961

Category: Mathematics

Page: 384

View: 9847

The Novikov conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes give a snapshot of the status of work on the Novikov conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, and analysis. Volume 1 contains a detailed historical survey and bibliography of the Novikov conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg. Volume 2 contains fundamental long research papers by G. Carlsson on "Bounded K-theory and the assembly map in algebraic K-theory" and by S. Ferry and E. Pedersen on "Epsilon surgery theory"; and shorter research and survey papers on various topics related to the Novikov conjecture, by Bekka, Cherix, Valette, Eichhorn, and others. These volumes will appeal to researchers interested in learning more about this intriguing area.

High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

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Author: Andrew Ranicki

Publisher: Springer Science & Business Media

ISBN: 3662120119

Category: Mathematics

Page: 646

View: 3910

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.

Topology, Geometry, and Algebra

Interactions and New Directions : Conference on Algebraic Topology in Honor of R. James Milgram, August 17-21, 1999, Stanford University

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Author: R. James Milgram,Alejandro Adem,Gunnar Carlsson,Ralph L. Cohen

Publisher: American Mathematical Soc.

ISBN: 082182063X

Category: Mathematics

Page: 255

View: 8226

This volume presents the proceedings from the conference on ``Topology, Geometry, and Algebra: Interactions and New Directions'' held in honor of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgery theory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of interaction between the different areas.

Documenta Mathematica

Journal Der Deutschen Mathematiker-Vereinigung

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8842

Surveys on Surgery Theory

Papers Dedicated to C.T.C. Wall

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Author: Sylvain Cappell,Sylvain F. Cappell,Andrew Ranicki,Jonathan Rosenberg

Publisher: N.A

ISBN: 9780691088150

Category: Mathematics

Page: 436

View: 6875

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.

Third International Congress of Chinese Mathematicians

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Author: Ka-Sing Lau,Zhouping Xin,Shing-Tung Yau

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 874

View: 4791

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.

Ends of Complexes

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Author: Bruce Hughes,Andrew Ranicki

Publisher: Cambridge University Press

ISBN: 9780521576253

Category: Mathematics

Page: 353

View: 9441

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

Dynamical Systems and Semisimple Groups

An Introduction

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Author: Renato Feres,RENATO AUTOR FERES

Publisher: Cambridge University Press

ISBN: 9780521591621

Category: Mathematics

Page: 245

View: 2527

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.

Geometry & Topology

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: N.A

View: 4419

Fully refereed international journal dealing with all aspects of geometry and topology and their applications.