Twisted tensor products related to the cohomology of the classifying spaces of loop groups

Abstract

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.