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This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics. The papers cover a wide range of topological specialties, including tools for the analysis of group actions on manifolds, calculations of algebraic K-theory, a result on analytic structures on Lie group actions, a presentation of the significance of Dirac operators in smoothing theory, a discussion of the stable topology of 4-manifolds, an answer to the famous question about symmetries of simply connected manifolds, and a fresh perspective on the topological classification of linear transformations.
The contributors include A. Adem, A. H. Assadi, M. Bökstedt, S. E. Cappell, R. Charney, M. W. Davis, P. J. Eccles, M. H. Freedman, I. Hambleton, J. C. Hausmann, S. Illman, G. Katz, M. Kreck, W. Lück, I. Madsen, R. J. Milgram, J. Morava, E. K. Pedersen, V. Puppe, F. Quinn, A. Ranicki, J. L. Shaneson, D. Sullivan, P. Teichner, Z. Wang, and S. Weinberger.
List of contents
| Foreword | |
| Program of the conference | |
| Mathematical descendants of William Browder | |
| The mod 2 cohomology rings of rank 3 simple group are Cohen Macaulay | 3 |
| Algebraic geometric invariants for homotopy actions | 13 |
| Algebraic K-theory of local number fields: the unramified case | 28 |
| The mapping cone and cylinder of a stratified map | 58 |
| Replacement of fixed sets and of their normal representations in transformation groups of manifolds | 67 |
| Finite K ([pi],,1)s for Artin groups | 110 |
| Double point manifolds of immersions of spheres in Euclidean space | 125 |
| Controlled linear algebra | 138 |
| Non-linear similarity revisited | 157 |
| On the Vietoris-Rips complexes and a cohomology theory for metric spaces | 175 |
| Every proper smooth action of a Lie group is equivalent to a real analytic action: a contribution to Hilbert's fifth problem | 189 |
| Formal deformations of equivariant genera, fixed point formula and universal symmetry blocks | 221 |
| Stable prime decompositions of four-manifolds | 251 |
| Smooth correspondences | 270 |
| Simply connected 6-dimensional manifolds with little symmetry and algebras with small tangent space | 283 |
| Speculations on Grommov convergence of stratified sets, and Riemannian volume collapse | 303 |
| Bordism of automorphisms of manifolds from the algebraic L-theory point of view | 314 |
| Exterior d, the local degree, and smoothability | 328 |
| Contributors | 339 |
About the author
Frank Quinn is University Distinguished Professor of Mathematics at Virginia Polytechnic Institute and State University.
Summary
This collection brings together papers by mathematicians exploring the research frontiers of topology. The book covers a wide range of topological specialities.
