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Diagram Cohomology and Isovariant Homotopy Theory
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Diagram Cohomology and Isovariant Homotopy Theory (Paperback)

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Synopsis

In algebraic topology, obstruction theory provides a way to study homotopy classes of continuous maps in terms of cohomology groups; a similar theory exists for certain spaces with group actions and maps that are compatible (that is, equivariant) with respect to the group actions. This work provides a corresponding setting for certain spaces with group actions and maps that are compatible in a stronger sense, called isovariant. The basic idea is to establish an equivalence between isovariant homotopy and equivariant homotopy for certain categories of diagrams. Consequences include isovariant versions of the usual Whitehead theorems for recognizing homotopy equivalences, an obstruction theory for deforming equivariant maps to isovariant maps, rational computations for the homotopy groups of certain spaces of isovariant functions, and applications to constructions and classification problems for differentiable group actions.

Science & MathematicsMathematicsGroups & group theoryScience & MathematicsMathematicsTopologyAlgebraic topology Publisher: American Mathematical Society Publication Date: 15/08/1994 ISBN-13: 9780821825891  Details: Type: Paperback Format: Books
Availability: To Order. Estimated despatch in 3-5 weeks.  

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