Twisted tensor products related to the cohomology of the classifying spaces of loop groups
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Bibliographic Information
Twisted tensor products related to the cohomology of the classifying spaces of loop groups
（Memoirs of the American Mathematical Society, no. 849）
American Mathematical Society, c2006
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Includes bibliographical references (p. 83-85)
"Volume 180, number 849 (third of 5 numbers)"
Description and Table of Contents
Description
Let $G$ be a compact, simply connected, simple Lie group. By applying the notion of a twisted tensor product in the senses of Brown as well as of Hess, we construct an economical injective resolution to compute, as an algebra, the cotorsion product which is the $E_2$-term of the cobar type Eilenberg-Moore spectral sequence converging to the cohomology of classifying space of the loop group $LG$. As an application, the cohomology $H^*(BLSpin(10); \mathbb{Z}/2)$ is explicitly determined as an $H^*(BSpin(10); \mathbb{Z}/2)$-module by using effectively the cobar type spectral sequence and the Hochschild spectral sequence, and further, by analyzing the TV-model for $BSpin(10)$.
Table of Contents
- Introduction The mod 2 cohomology of $BLSO(n)$ The mod 2 cohomology of $BLG$ for $G=Spin(n)\ (7\leq n\leq 9)$ The mod 2 cohomology of $BLG$ for $G=G_2,F_4$ A multiplication on a twisted tensor product The twisted tensor product associated with $H^*(Spin(N)
- \mathbb{Z}/2)$ A manner for calculating the homology of a DGA The Hochschild spectral sequence Proof of Theorem 1.6 Computation of a cotorsion product of $H^*(Spin(10)
- \mathbb{Z}/2)$ and the Hochschild homology of $H^*(BSpin(10)
- \mathbb{Z}/2)$ Proof of Theorem 1.7 Proofs of Proposition 1.9 and Theorem 1.10 Appendix Bibliography.
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