It takes the average reader 3 hours and 3 minutes to read Generalized Tate Cohomology by John Patrick Campbell Greenlees
Assuming a reading speed of 250 words per minute. Learn more
This book presents a 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. Special cases include Tate-Swan cohomology when $G$ is finite and a version of cyclic cohomology when $G = S^1$. The groups $t(k_G)^*(X)$ are obtained by suitably splicing the $k$-homology with the $k$-cohomology of the Borel construction $EG\times _G X$, where $k^*$ is the nonequivariant cohomology theory that underlies $k^*_G$. 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. When $G$ is finite, the Tate theory associated to equivariant $K$-theory is calculated completely, and the Tate theory associated to equivariant cohomotopy is shown to encode a mysterious web of connections between the Tate cohomology of finite groups and the stable homotopy groups of spheres.
Generalized Tate Cohomology by John Patrick Campbell Greenlees is 178 pages long, and a total of 45,924 words.
This makes it 60% the length of the average book. It also has 56% more words than the average book.
The average oral reading speed is 183 words per minute. This means it takes 4 hours and 10 minutes to read Generalized Tate Cohomology aloud.
Generalized Tate Cohomology is suitable for students ages 10 and up.
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