Crossed simplicial groups of framed braids and mapping class groups of surfaces
type: Item
instance of: scholarly article
title: Crossed simplicial groups of framed braids and mapping class groups of surfaces
zbMATH Open document ID: 0898.18006
DOI: 10.1007/BF02986853
published in: Lithuanian Mathematical Journal
publication date: 1997-10-30T00:00:00Z
review text: It is well known that the geometric realization of a cyclic crossed simplicial group is homeomorphic to the circle. The author associates with a surface the crossed simplicial groups \(FB^P_\bullet(M)\) and \(FMC^P_\bullet(M)\) of framed braids and framed mapping class groups. Then their homotopy type is calculated and, in particular, isomorphisms \(FB^P_\bullet(S^2)\simeq SU(2)\) and \(FMC^P_\bullet(S^2)\simeq SO(3)\) are deduced [cf. the author, 34-th Conf. of Lith. Math. Soc., Vilnius, 53-54 (1993)].
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 57M99
zbMATH DE Number: 1059788
zbMATH Keywords: crossed simplicial group
zbMATH Keywords: braid group
zbMATH Keywords: \(n\)-configuration
zbMATH Keywords: Lie group
zbMATH Keywords: surface
zbMATH Keywords: framed mapping class groups
author: R. Krasauskas
reviewed by: Marek Golasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1059788