Algebraic L-theory and Topological Manifolds


Author: A. A. Ranicki
Publisher: Cambridge University Press
ISBN: 9780521420242
Category: Mathematics
Page: 358
View: 6268
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"However, research mathematicians applying ideas from algebraic and geometric topology in areas such as number theory or algebra will also benefit from this authoritative account."--BOOK JACKET.

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: 834
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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: 1999
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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.

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: 6119
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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.

Ends of Complexes


Author: Bruce Hughes,Andrew Ranicki
Publisher: Cambridge University Press
ISBN: 9780521576253
Category: Mathematics
Page: 353
View: 4090
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A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.

Lower K- and L-theory


Author: Andrew Ranicki
Publisher: Cambridge University Press
ISBN: 9780521438018
Category: Mathematics
Page: 174
View: 8428
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This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author.

Surveys on Surgery Theory

Papers Dedicated to C.T.C. Wall
Author: Sylvain E. Cappell,Charles Terence Clegg Wall,Andrew Ranicki,Jonathan R​osenberg
Publisher: Princeton University Press
ISBN: 9780691049380
Category: Mathematics
Page: 448
View: 6572
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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.

Sūgaku Expositions

A Translation of Sūgaku
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 7664
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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: 5827
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Algebraic and Geometric Topology


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Algebraic topology
Page: N.A
View: 6143
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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: 3094
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Floer Homology Groups in Yang-Mills Theory


Author: S. K. Donaldson
Publisher: Cambridge University Press
ISBN: 9781139432603
Category: Mathematics
Page: N.A
View: 5341
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The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.

Geometry, Analysis and Topology of Discrete Groups


Author: Lizhen Ji
Publisher: International Pressof Boston Incorporated
ISBN: 9781571461261
Category: Mathematics
Page: 468
View: 2121
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Discrete subgroups of Lie groups are foundational objects in modern mathematics and occur naturally in different subjects. This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory, and topology. Most of the papers are surveys, and the volume is intended to help graduate students and researchers better understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.

London Mathematical Society lecture note series


Author: Andrew Ranicki
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 2708
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Documenta Mathematica

Journal Der Deutschen Mathematiker-Vereinigung
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 1790
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Geometry & Topology


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Geometry
Page: N.A
View: 9046
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Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

Surgery on Compact Manifolds


Author: Charles Terence Clegg Wall,Andrew Ranicki
Publisher: American Mathematical Soc.
ISBN: 0821809423
Category: Mathematics
Page: 302
View: 4549
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The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.

Monopoles and Three-Manifolds


Author: Peter Kronheimer,Tomasz Mrowka
Publisher: Cambridge University Press
ISBN: 1139468669
Category: Mathematics
Page: N.A
View: 3758
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Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg–Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg–Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides a full discussion of a central part of the study of the topology of manifolds.

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: 608
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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.

Mappings and dimension


Author: V. I. Arnold
Publisher: N.A
ISBN: N.A
Category: Dimension theory (Topology)
Page: 229
View: 7038
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