Involutions on S[ΩM]

الأصل · EN

The contribution of this PhD thesis is to construct for each vector bundle ξ an orthogonal ring spectrum R, weakly equivalent to S[ΩM], together with an involution on R. On the homotopy groups π*S[ΩM] our involution corresponds to parallel transportation in ξ, and reversing loops in M. The main result is theorem 4.3.26. The orthogonal ring spectrum R with involution is intended as input for LA, K, TC and THH, the ultimate goal is to compute homotopy groups of automorphism groups. We take a first step in this direction by considering the definition and a few basic properties of TC(L) and THH(L) for arbitrary orthogonal ring spectra L (with involution).