Author: M. DavisPublisher: Springer
ISBN: 3540359117
Category : Mathematics
Languages : en
Pages : 150
Book Description
Multiaxial Actions on Manifolds
Author: M. DavisPublisher: Springer
ISBN: 3540359117
Category : Mathematics
Languages : en
Pages : 150
Book Description
Multiaxial actions on manifolds
Author: Michael DavisGroup Actions on Manifolds
Author: Reinhard SchultzPublisher: American Mathematical Soc.
ISBN: 0821850385
Category : Mathematics
Languages : en
Pages : 586
Book Description
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.
MULTIAXIAL ACTIONS ON MANIFOLDS- BASED ON PAPERS PRESENTED AT THE TRANSFORMATION GROUPS SEMINAR.
Author: Topological Classification of Some Multiaxial Actions on Spheres and Products
Author: Jared Alexander BassPublisher:
ISBN: 9781303228544
Category :
Languages : en
Pages : 63
Book Description
A multiaxial U(n)-manifold is defined to be a manifold with a U(n) action whose local orbit structure is governed by a multiple of the defining representation of U(n) on C n plus a multiple of the trivial representation. This thesis builds on earlier work of M. Davis and W. C. Hsiang in the smooth category and S. Cappell, S. Weinberger, and M. Yan in the topological category and gives some new results about the topological classification of multiaxial actions on spheres and on certain product manifolds. Our results allow for a proof of the injectivity of the suspension map (first observed for the n = 1 case by Rothenberg and Sullivan) and a complete analysis of desuspension obstructions, and rely on specific calculations of homology of orbit spaces and also a Kunneth formula for L (e)-cohomology.
Computers, Rigidity, and Moduli
Author: Shmuel WeinbergerPublisher: Princeton University Press
ISBN: 0691222460
Category : Mathematics
Languages : en
Pages : 190
Book Description
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity. II
Author: Eldar StraumePublisher: American Mathematical Soc.
ISBN: 0821804839
Category : Mathematics
Languages : en
Pages : 90
Book Description
The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E. D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres.
A Fête of Topology
Author: Y. MatsumotoPublisher: Academic Press
ISBN: 1483259188
Category : Mathematics
Languages : en
Pages : 615
Book Description
A Fête of Topology: Papers Dedicated to Itiro Tamura focuses on the progress in the processes, methodologies, and approaches involved in topology, including foliations, cohomology, and surface bundles. The publication first takes a look at leaf closures in Riemannian foliations and differentiable singular cohomology for foliations. Discussions focus on differentiable singular chains restricted to leaves, differentiable singular cohomology for foliations, covering of pseudogroups and fundamental group, normal type of an orbit closure, and construction of a global model. The text then takes a look at measure of exceptional minimal sets of codimension one foliations, examples of exceptional minimal sets, foliations transverse to non-singular Morse-Smale flows, and Chern character for discrete groups. The manuscript ponders on characteristic classes of surface bundles and bounded cohomology, Hill's equation, isomonodromy deformation and characteristic classes, and topology of folds, cusps, and Morin singularities. Topics include system of Hill's equations, Lagrange-Grassman manifold, positive curves, Morse theory, bounded cohomology, and characteristic classes of surface bundles. The publication is a vital source of information for researchers interested in topology.
Equivariant Surgery Theories and Their Periodicity Properties
Author: Karl H. DovermannPublisher: Springer
ISBN: 3540463941
Category : Mathematics
Languages : en
Pages : 234
Book Description
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.
Prospects in Topology (AM-138), Volume 138
Author: Frank QuinnPublisher: Princeton University Press
ISBN: 1400882583
Category : Mathematics
Languages : en
Pages : 340
Book Description
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.