Memoirs of the American Mathematical Society 1994; 82 pp; softcover Volume: 110 ISBN10: 0821825895 ISBN13: 9780821825891 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/110/527
 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. Readership Research mathematicians. Table of Contents  Introduction
 Equivariant homotopy in diagram categories
 Quasistratifications
 Isovariant homotopy and maps of diagrams
 Almost isovariant maps
 Obstructions to isovariance
 Homotopy groups of isovariant function spaces
 Calculations with the spectral sequence
 Applications to differentiable group actions
 Index of selected terms and symbols
 References
