Thom Spectra of Generalized Braid Groups
Vladimir V. Vershinin
Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
It is proved that Thom spectra of generalized braid groups are the wedges of
suspensions over the Eilenberg-MacLane spectrum for Z/2. Precise structure of
the Thom spectra of the generalized braid groups of the types C and D is
obtained. For the generalized braid groups of type C the natural pairing
analogous to the pairing of the classical braids is studied. This paring
generates the multiplicative structure of the Thom spectrum such that the
corresponding bordism theory has the coefficient ring isomorphic to the
polynomial ring over Z/2 on one generator of dimension one: Z/2[s].