Algebraic L-theory and Topological Manifolds


Author: A. A. Ranicki
Publisher: Cambridge University Press
ISBN: 9780521420242
Category: Mathematics
Page: 358
View: 6230
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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, Bruce E. Williams
Publisher: American Mathematical Soc.
ISBN: 147040981X
Category: Mathematics
Page: 110
View: 8131
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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

Algebraic Surgery in Codimension 2
Author: Andrew Ranicki
Publisher: Springer Science & Business Media
ISBN: 3662120119
Category: Mathematics
Page: 646
View: 9917
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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.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Oberwolfach 1993
Author: Steven C. Ferry
Publisher: Cambridge University Press
ISBN: 9780521497961
Category: Mathematics
Page: 384
View: 9821
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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.

Topology, Geometry, and Algebra

Interactions and New Directions : Conference on Algebraic Topology in Honor of R. James Milgram, August 17-21, 1999, Stanford University
Author: R. James Milgram,Alejandro Adem,Gunnar Carlsson,Ralph L. Cohen
Publisher: American Mathematical Soc.
ISBN: 082182063X
Category: Mathematics
Page: 255
View: 1920
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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.

Schriftenreihe des Mathematischen Instituts der Universität Münster


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 8745
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Bulletin of the Belgian Mathematical Society, Simon Stevin


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 3564
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Bulletin (new Series) of the American Mathematical Society


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 3018
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London Mathematical Society lecture note series


Author: Andrew Ranicki
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 352
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Surveys on Surgery Theory

Papers Dedicated to C.T.C. Wall
Author: Sylvain Cappell,Sylvain F. Cappell,Andrew Ranicki,Jonathan Rosenberg
Publisher: N.A
ISBN: 9780691088150
Category: Mathematics
Page: 436
View: 1061
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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.

Sūgaku Expositions

A Translation of Sūgaku
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 5559
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Third International Congress of Chinese Mathematicians


Author: Ka-Sing Lau,Zhouping Xin,Shing-Tung Yau
Publisher: Amer Mathematical Society
ISBN: N.A
Category: Mathematics
Page: 874
View: 4292
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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.

Bulletin of the American Mathematical Society


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 8879
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Mappings and dimension


Author: V. I. Arnold
Publisher: N.A
ISBN: N.A
Category: Dimension theory (Topology)
Page: 229
View: 1283
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Ends of Complexes


Author: Bruce Hughes,Andrew Ranicki
Publisher: Cambridge University Press
ISBN: 9780521576253
Category: Mathematics
Page: 353
View: 6931
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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
Author: Renato Feres,RENATO AUTOR FERES
Publisher: Cambridge University Press
ISBN: 9780521591621
Category: Mathematics
Page: 245
View: 7883
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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.

Mixed Hodge Structures and Singularities


Author: Valentine S. Kulikov,Valentin Stepanovič Kulikov
Publisher: Cambridge University Press
ISBN: 9780521620604
Category: Mathematics
Page: 186
View: 3119
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This vital work is both an introduction to, and a survey of singularity theory, in particular, studying singularities by means of differential forms. Here, some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss-Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This is an excellent resource for all researchers in singularity theory, algebraic or differential geometry.

Vorlesungen Über Inhalt, Oberfläche und Isoperimetrie


Author: Hugo Hadwiger
Publisher: Springer-Verlag
ISBN: 3642947026
Category: Mathematics
Page: 312
View: 4296
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Oberflächen


Author: Hubert Brian Griffiths
Publisher: N.A
ISBN: N.A
Category: Surfaces
Page: 147
View: 8093
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Neue Topologische Methoden in der Algebraischen Geometrie


Author: Friedrich Hirzebruch
Publisher: Springer-Verlag
ISBN: 3662410834
Category: Mathematics
Page: 165
View: 1607
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