Generalized Tate Cohomology (Memoirs of the AMS) by J. P. C. Greenlees (PDF)

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This book presents a full and systematic study of a new equivariant cohomology theory t(k[G)* constructed from any given equivariant cohomology theory k*[G, where G is a compact Lie group. The new theories play a central role in relating equivariant algebraic topology with current areas of interest in nonequivariant algebraic topology. Their study is essential to a full understanding of such “completion theorems” as the Atiyah-Segal completion theorem in K-theory and the Segal conjecture in cohomotopy.

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