Thom spectra of the commutator subgroups of the generalized braid groups
Brieskorn generalized the notion of braid group to finite Coxeter groups. Thus for the series of Coxeter groups corresponding to the Coxeter graphs \(C_{n}\) and \(D_{n}\) one obtains groups \(Br(C_{n})\) and \(Br(D_{n})\) respectively. The commutator groups \([Br(C_{n}),Br(C_{n})]\) and \([Br(D_{n}),Br(D_{n})]\) are canonically embedded into the group \(SO_{n}\). The paper determines the homotopy type of the plus-construction of the classifying spaces for these commutator subgroups and for the Thom spectra induced by the embeddings.
scientific article; zbMATH DE number 1407560
scientific article