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Differential Topology, Foliations, and Group Actions
Edited by: Paul A. Schweitzer, S. J., Pontificia Universidade Catolica, Rio de Janeiro, Brazil, Steven Hurder, University of Illinois, Chicago, Nathan Moreira dos Santos, Universidade Federal Fluminense, Niteroi, Brazil, and José Luis Arraut, USP-ICMSE, Sao Carlos, Brazil
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Contemporary Mathematics
1994; 287 pp; softcover
Volume: 161
ISBN-10: 0-8218-5170-5
ISBN-13: 978-0-8218-5170-8
List Price: US$43
Member Price: US$34.40
Order Code: CONM/161
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This volume contains the proceedings of the Workshop on Topology held at the Pontifícia Universidade Católica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions--finite group actions and rigidity theory for Anosov actions--as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.

Readership

Researchers and graduate students in topology and related fields.

Table of Contents

  • Foliations
  • J. Cantwell and L. Conlon -- Topological obstructions to smoothing proper foliations
  • O. Calvo-Andrade -- Deformations of holomorphic foliations
  • S. Hurder and Y. Mitsumatsu -- Transverse Euler classes of foliations on non-atomic foliation cycles
  • N. M. d. Santos -- Foliated cohomology and characteristic classes
  • R. Langevin -- A list of questions about foliations
  • De Rham theory and singularities
  • A. G. Aleksandrov -- Duality and De Rham complex on singular varieties
  • J.-P. Brasselet -- De Rham theorems for singular varieties
  • M. A. S. Ruas -- On the equisingularity of families of corank \(1\) generic germs
  • Two surveys on actions
  • A. Adem -- Cohomology and actions of finite groups
  • S. Hurder -- A survey of rigidity theory for Anosov actions
  • Low-dimensional topology
  • N. C. Saldanha -- An introduction to geometric topology: Geometric structures on manifolds of dimensions \(2\) and \(3\)
  • D. Randall -- On \(4\)-dimensional bundle theories
  • D. Randall and P. A. Schweitzer S. J. -- On foliations, concordance spaces, and the Smale conjectures
  • J. N. Ballesteros and M. C. R. Fuster -- Generic \(1\)-parameter families of closed space curves
  • Characteristic classes
  • J. L. Dupont and F. W. Kamber -- Dependence relations for Cheeger-Chern-Simons invariants of locally symmetric spaces
  • N. E. Barufatti -- Obstructions to immersions of projective Stiefel manifolds
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