Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups

Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups
ISBN-10
0821838563
ISBN-13
9780821838563
Category
Cohomology operations
Pages
98
Language
English
Published
2006
Publisher
American Mathematical Soc.
Authors
Katsuhiko Kuribayashi, Mamoru Mimura, Tetsu Nishimoto

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 $BSpin(10)$.

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