Memoirs of the American Mathematical Society 2006; 85 pp; softcover Volume: 180 ISBN10: 0821838563 ISBN13: 9780821838563 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/180/849
 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 EilenbergMoore 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 TVmodel 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
