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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On homological properties of singular braids
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by Vladimir V. Vershinin PDF
Trans. Amer. Math. Soc. 350 (1998), 2431-2455 Request permission


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.
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Additional Information
  • Vladimir V. Vershinin
  • Affiliation: Institute of Mathematics, Novosibirsk, 630090, Russia
  • Email:
  • 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:
  • MathSciNet review: 1443895