Braid groups, mapping class groups and their homology with twisted coefficients

DOI10.1017/S0305004121000219zbMath1487.55021arXiv1901.08028OpenAlexW3143281722MaRDI QIDQ5063189

Andrea Bianchi

Publication date: 17 March 2022

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.08028

zbMATH Keywords

homologymapping class grouptwisted coefficientsbraid grouphomological stabilitysymplectic representation

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Homology with local coefficients, equivariant cohomology (55N25) Spectral sequences and homology of fiber spaces in algebraic topology (55R20) Maps between classifying spaces in algebraic topology (55R37) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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• Stability of the homology of the mapping class groups of orientable surfaces
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• Braids, mapping class groups, and categorical delooping
• Teichmüller theory for surfaces with boundary
• On isotopies of homeomorphisms of Riemann surfaces
• Resolutions of moduli spaces and homological stability
• Thom Spectra of Generalized Braid Groups
• Embeddings of braid groups into mapping class groups and their homology
• Configuration Spaces.

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