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| Author | : Karl Heinz Dovermann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 132 |
| Release | : 1988 |
| Genre | : Cobordism theory |
| ISBN | : 0821824422 |
In 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 | : Karl H. Dovermann |
| Publisher | : Springer |
| Total Pages | : 234 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540463941 |
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theory for advanced graduate students and researchers in related areas, or as an account of the authors' previously unpublished work on periodicity for specialists in surgery theory or transformation groups.
| Author | : Reinhard Schultz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 586 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821850385 |
Presents 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 | : Stefan Jackowski |
| Publisher | : Springer |
| Total Pages | : 404 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354047403X |
As 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.
| Author | : Selman Akbulut |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 170 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821802925 |
This book contains the proceedings of the Real Algebraic Geometry-Topology Conference, held at Michigan State University in December 1993. Presented here are recent results and discussions of new ideas pertaining to such topics as resolution theorems, algebraic structures, topology of nonsingular real algebraic sets, and the distribution of real algebraic sets in projective space.
| Author | : Katsuo Kawakubo |
| Publisher | : Springer |
| Total Pages | : 406 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540461787 |
| Author | : Nigel Higson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 212 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9780821838464 |
In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ``ordinary'' geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the ``residue index theorem'' of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
| Author | : Shmuel Weinberger |
| Publisher | : University of Chicago Press |
| Total Pages | : 314 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9780226885667 |
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.
| Author | : American Mathematical Society |
| Publisher | : |
| Total Pages | : 810 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Anthony Bak |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 272 |
| Release | : 2002-07-31 |
| Genre | : Mathematics |
| ISBN | : 9781402007835 |
This 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.
