On homological properties of singular braids

Author:
Vladimir V. Vershinin

Journal:
Trans. Amer. Math. Soc. **350** (1998), 2431-2455

MSC (1991):
Primary 20J05, 20F36, 20F38, 18D10, 55P35

DOI:
https://doi.org/10.1090/S0002-9947-98-02048-0

MathSciNet review:
1443895

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Abstract: Homology of objects which can be considered as singular braids, or braids with crossings, is studied. Such braids were introduced in connection with Vassiliev's theory of invariants of knots and links. The corresponding algebraic objects are the braid-permutation group of R. Fenn, R. Rimányi and C. Rourke and the Baez-Birman monoid which embeds into the singular braid group . The following splittings are proved for the plus-constructions of the classifying spaces of the infinite braid-permutation group and the singular braid group

where is an infinite loop space and is a double loop space.

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Additional Information

**Vladimir V. Vershinin**

Affiliation:
Institute of Mathematics, Novosibirsk, 630090, Russia

Email:
versh@math.nsc.ru

DOI:
https://doi.org/10.1090/S0002-9947-98-02048-0

Keywords:
Braid group,
permutation group,
homology,
classifying space,
loop space

Received by editor(s):
August 20, 1996

Article copyright:
© Copyright 1998
American Mathematical Society