Diagram Cohomology and Isovariant Homotopy Theory

Released on by Giora Dula
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  • Diagram Cohomology and Isovariant Homotopy Theory Book Detail

  • Author : Giora Dula
  • Release Date : 1994
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 97
  • ISBN 13 : 0821825895
  • File Size : 99,99 MB
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Diagram Cohomology and Isovariant Homotopy Theory by Giora Dula PDF Summary

Book Description: Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.

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Intersection Pairings on Conley Indices

Intersection Pairings on Conley Indices

File Size : 37,37 MB
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This memoir is a careful and detailed study of the intersection pairing in the Conley index. The Conley index associates to an isolated invariant set of a semif