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Author: Karl Heinz Dovermann
Publisher: American Mathematical Soc.
Published: 1988
Total Pages: 132
ISBN-13: 0821824422
DOWNLOAD EBOOKIn this work we develop an equivariant Sullivan-Wall surgery exact sequence in the category of smooth and locally linear actions of finite groups which satisfy the gap hypothesis. We then apply this machinery to various problems of classifying group actions on manifolds.
Author: Reinhard Schultz
Publisher: American Mathematical Soc.
Published: 1985
Total Pages: 586
ISBN-13: 0821850385
DOWNLOAD EBOOKPresents an understanding of the sorts of problems one studies in group actions and the methods used to study such problems. This book features articles based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.
Author: Karl H. Dovermann
Publisher: Springer
Published: 2006-11-14
Total Pages: 234
ISBN-13: 3540463941
DOWNLOAD EBOOKThe 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theory for advanced graduate students and researchers in related areas, or as an account of the authors' previously unpublished work on periodicity for specialists in surgery theory or transformation groups.
Author: Katsuo Kawakubo
Publisher: Springer
Published: 2006-11-14
Total Pages: 406
ISBN-13: 3540461787
DOWNLOAD EBOOKAuthor: Sylvain Cappell
Publisher: Princeton University Press
Published: 2014-09-08
Total Pages: 446
ISBN-13: 1400865212
DOWNLOAD EBOOKSurgery 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.
Author: Ulrich Koschorke
Publisher: Springer
Published: 2006-12-08
Total Pages: 507
ISBN-13: 3540391878
DOWNLOAD EBOOKAuthor: Shmuel Weinberger
Publisher: University of Chicago Press
Published: 1994
Total Pages: 314
ISBN-13: 9780226885667
DOWNLOAD EBOOKThis 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.
Author: Andrew Ranicki
Publisher: Springer
Published: 2006-11-14
Total Pages: 428
ISBN-13: 3540394133
DOWNLOAD EBOOKAuthor: Anthony Bak
Publisher: Springer Science & Business Media
Published: 2002-07-31
Total Pages: 272
ISBN-13: 9781402007835
DOWNLOAD EBOOKThis book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.
Author: Stefan Jackowski
Publisher: Springer
Published: 2006-11-14
Total Pages: 404
ISBN-13: 354047403X
DOWNLOAD EBOOKAs part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
