Homology ring mod 2 of free loop groups of spinor groups (Q1970730)

Let \(G\) be a compact connected Lie group and denote by \(\Omega G\) its based loop space. The free loop group \(LG(G)\) of \(G\) is the topological group of all continuous maps from \(S^1\) to \(G\). The group \(LG(G)\) is the semidirect product of \(\Omega G\) and \(G\). Denote by Ad the pointwise adjoint action of \(G\) on \(\Omega G\). The author computes the induced map \(\text{Ad}_*\) at the homology level, in the case where \((G,p)=(\text{Spin}(N),p)\) and studies the mod 2 homology of \(LG(\text{Spin}(N))\), establishing a relationship with the Hopf algebra structure.