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Journal of the London Mathematical Society 2000 61(1):245-258; doi:10.1112/S0024610799008091
© 2000 by London Mathematical Society
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© The London Mathematical Society

Thom Spectra of Generalized Braid Groups

Vladimir V. Vershinin

Sobolev Institute of Mathematics Novosibirsk 630090, Russia, versh{at}math.nsc.ru

Received 3 January 1997.

It is proved that Thom spectra of generalized braid groups are the wedges of suspensions over the Eilenberg–MacLane spectrum for Z/2. The 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 pairing 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 1:Z/2[s].


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