On homological properties of singular braids
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- by Vladimir V. Vershinin
- Trans. Amer. Math. Soc. 350 (1998), 2431-2455
- DOI: https://doi.org/10.1090/S0002-9947-98-02048-0
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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 $BP_{n}$ of R. Fenn, R. Rimányi and C. Rourke and the Baez-Birman monoid $SB_{n}$ which embeds into the singular braid group $SG_{n}$. The following splittings are proved for the plus-constructions of the classifying spaces of the infinite braid-permutation group and the singular braid group \begin{equation*} \mathbb {Z}\times BBP_{\infty }^{+}\simeq \Omega ^{\infty }S^{\infty }\times S^{1} \times Y, \end{equation*} \begin{equation*} \mathbb {Z}\times BSG_{\infty }^{+}\simeq S^{1}\times \Omega ^{2} S^{2}\times W, \end{equation*} where $Y$ is an infinite loop space and $W$ is a double loop space.References
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Bibliographic Information
- Vladimir V. Vershinin
- Affiliation: Institute of Mathematics, Novosibirsk, 630090, Russia
- Email: versh@math.nsc.ru
- Received by editor(s): August 20, 1996
- © Copyright 1998 American Mathematical Society
- 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