Induction Theorems for Groups of Homotopy Manifold Structures

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Publisher : American Mathematical Soc.
ISBN 13 : 0821822675
Total Pages : 117 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Induction Theorems for Groups of Homotopy Manifold Structures by : Andrew J. Nicas

Download or read book Induction Theorems for Groups of Homotopy Manifold Structures written by Andrew J. Nicas and published by American Mathematical Soc.. This book was released on 1982 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classifying spaces in surgery theory were first used by Sullivan and Casson in their (independent) unpublished work on the Hauptvermutung for PL manifolds. In his 1968 Ph.D. thesis, F. Quinn developed a general theory of surgery classifying spaces, realizing the Wall surgery groups as the homotopy groups [italic]L[subscript]*([italic]G) = [lowercase Greek]Pi[subscript]*([italic]L([italic]G)) of a spectrum of manifold n-ad surgery problems with fundamental group G. This work presents a detailed account of Quinn's theory. Geometric methods are used to view the Sullivan-Wall manifold structure sequence as an exact sequence of abelian groups (as suggested by Quinn). The intersection of the known induction theorems for generalized cohomology groups and [italic]L-groups then gives an induction theorem for the structure sequence with finite [italic]G.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

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Publisher : Cambridge University Press
ISBN 13 : 0521497965
Total Pages : 386 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Novikov Conjectures, Index Theorems, and Rigidity: Volume 1 by : Steven C. Ferry

Download or read book Novikov Conjectures, Index Theorems, and Rigidity: Volume 1 written by Steven C. Ferry and published by Cambridge University Press. This book was released on 1995-11-23 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

Combinatorial Group Theory and Topology

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Publisher : Princeton University Press
ISBN 13 : 9780691084107
Total Pages : 568 pages
Book Rating : 4.0/5 (841 download)

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Book Synopsis Combinatorial Group Theory and Topology by : S. M. Gersten

Download or read book Combinatorial Group Theory and Topology written by S. M. Gersten and published by Princeton University Press. This book was released on 1987-05-21 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.

Canadian Journal of Mathematics

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Publisher :
ISBN 13 :
Total Pages : 258 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Mathematics by :

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1987-02 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Algebraic Characterization of Geometric 4-Manifolds

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Publisher : Cambridge University Press
ISBN 13 : 0521467780
Total Pages : 184 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis The Algebraic Characterization of Geometric 4-Manifolds by : J. A. Hillman

Download or read book The Algebraic Characterization of Geometric 4-Manifolds written by J. A. Hillman and published by Cambridge University Press. This book was released on 1994-02-03 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes work on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces.

Geometry and Topology

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Publisher : CRC Press
ISBN 13 : 9780824776213
Total Pages : 370 pages
Book Rating : 4.7/5 (762 download)

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Book Synopsis Geometry and Topology by : Mccrory

Download or read book Geometry and Topology written by Mccrory and published by CRC Press. This book was released on 1986-10-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

High-dimensional Manifold Topology

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Publisher : World Scientific
ISBN 13 : 9789812704443
Total Pages : 516 pages
Book Rating : 4.7/5 (44 download)

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Book Synopsis High-dimensional Manifold Topology by : R. T. Farrell

Download or read book High-dimensional Manifold Topology written by R. T. Farrell and published by World Scientific. This book was released on 2003 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers topics such as manifolds with positive scalar curvature, pseudo-isotopy spectrum and controlled theory, and reduction of the Novikov and Borel conjectures for aspherical complexes to aspherical manifolds.

High-dimensional Manifold Topology - Proceedings Of The School

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Publisher : World Scientific
ISBN 13 : 9814487074
Total Pages : 510 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis High-dimensional Manifold Topology - Proceedings Of The School by : F Thomas Farrell

Download or read book High-dimensional Manifold Topology - Proceedings Of The School written by F Thomas Farrell and published by World Scientific. This book was released on 2003-10-17 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.)Equivariant Cellular Homology and Its Applications (B Chorny)Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.)Chain Complex Invariants for Group Actions (L E Jones)The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.)The Surgery Exact Sequence Revisited (E K Pedersen)K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer)Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz)and other papers Readership: Graduate students and researchers in geometry and topology. Keywords:High-Dimensional Manifold Topology;Operator Algebras;K-Theory;L-Theory;Foliated Control Theory

Handbook of Geometric Topology

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Publisher : Elsevier
ISBN 13 : 0080532853
Total Pages : 1145 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Geometric Topology by : R.B. Sher

Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.

The Topological Classification of Stratified Spaces

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Publisher : University of Chicago Press
ISBN 13 : 9780226885674
Total Pages : 308 pages
Book Rating : 4.8/5 (856 download)

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Book Synopsis The Topological Classification of Stratified Spaces by : Shmuel Weinberger

Download or read book The Topological Classification of Stratified Spaces written by Shmuel Weinberger and published by University of Chicago Press. This book was released on 1994 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.

Equivariant Surgery Theories and Their Periodicity Properties

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Publisher : Springer
ISBN 13 : 3540463941
Total Pages : 234 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Equivariant Surgery Theories and Their Periodicity Properties by : Karl H. Dovermann

Download or read book Equivariant Surgery Theories and Their Periodicity Properties written by Karl H. Dovermann and published by Springer. This book was released on 2006-11-14 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of surgery on manifolds has been generalized to categories of manifolds with group actions in several different ways. This book discusses some basic properties that such theories have in common. Special emphasis is placed on analogs of the fourfold periodicity theorems in ordinary surgery and the roles of standard general position hypotheses on the strata of manifolds with group actions. The contents of the book presuppose some familiarity with the basic ideas of surgery theory and transformation groups, but no previous knowledge of equivariant surgery is assumed. The book is designed to serve either as an introduction to equivariant surgery theory for advanced graduate students and researchers in related areas, or as an account of the authors' previously unpublished work on periodicity for specialists in surgery theory or transformation groups.

Variations on a Theme of Borel

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Publisher : Cambridge University Press
ISBN 13 : 1107142598
Total Pages : 365 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Variations on a Theme of Borel by : Shmuel Weinberger

Download or read book Variations on a Theme of Borel written by Shmuel Weinberger and published by Cambridge University Press. This book was released on 2022-11-30 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Geometry and Topology

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Publisher : CRC Press
ISBN 13 : 1000153932
Total Pages : 370 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Geometry and Topology by : Martin A. Mccrory

Download or read book Geometry and Topology written by Martin A. Mccrory and published by CRC Press. This book was released on 2020-12-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

A Course on Surgery Theory

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Publisher : Princeton University Press
ISBN 13 : 0691200351
Total Pages : 472 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis A Course on Surgery Theory by : Stanley Chang

Download or read book A Course on Surgery Theory written by Stanley Chang and published by Princeton University Press. This book was released on 2021-01-26 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced treatment of surgery theory for graduate students and researchers Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest. Of significant use to high-dimensional topologists and researchers in noncommutative geometry and algebraic K-theory, A Course on Surgery Theory serves as an important resource for the mathematics community.

Nilpotence and Periodicity in Stable Homotopy Theory

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Publisher : Princeton University Press
ISBN 13 : 9780691025728
Total Pages : 228 pages
Book Rating : 4.0/5 (257 download)

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Book Synopsis Nilpotence and Periodicity in Stable Homotopy Theory by : Douglas C. Ravenel

Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Surveys on Surgery Theory

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Publisher : Princeton University Press
ISBN 13 : 9780691049380
Total Pages : 452 pages
Book Rating : 4.0/5 (493 download)

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Book Synopsis Surveys on Surgery Theory by : Sylvain E. Cappell

Download or read book Surveys on Surgery Theory written by Sylvain E. Cappell and published by Princeton University Press. This book was released on 2000-01-10 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Canadian Journal of Mathematics

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Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Mathematics by :

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1986-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: