Braids, mapping class groups, and categorical delooping

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dc.creatorSong, Yongjin
dc.creatorTillmann, Ulrike
dc.date2006-09-21
dc.date2007-05-10
dc.date.accessioned2026-07-07T08:00:31Z
dc.date.available2026-07-07T08:00:31Z
dc.descriptionDehn twists around simple closed curves in oriented surfaces satisfy the braid relations. This gives rise to a group theoretic from the braid group to the mapping class group. We prove here that this map is trivial in stable homology with any trivial coefficients. In particular this proves an old conjecture of J. Harer. The main tool is categorical delooping. In an appendix we discuss geometrically defined homomorphisms from the braid to the mapping class group.
dc.description19 pages, 9 figures, latex
dc.identifierhttps://arxiv.org/abs/math/0609597
dc.identifierhttp://arxiv.org/abs/math/0609597
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128683
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject55P48, 57M50, 55R37
dc.titleBraids, mapping class groups, and categorical delooping
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