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

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Braid groups, mapping class groups and their homology with twisted coefficients. / Bianchi, Andrea.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 172, No. 2, 2022, p. 249-266.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bianchi, A 2022, 'Braid groups, mapping class groups and their homology with twisted coefficients', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 172, no. 2, pp. 249-266. https://doi.org/10.1017/S0305004121000219

APA

Bianchi, A. (2022). Braid groups, mapping class groups and their homology with twisted coefficients. Mathematical Proceedings of the Cambridge Philosophical Society, 172(2), 249-266. https://doi.org/10.1017/S0305004121000219

Vancouver

Bianchi A. Braid groups, mapping class groups and their homology with twisted coefficients. Mathematical Proceedings of the Cambridge Philosophical Society. 2022;172(2):249-266. https://doi.org/10.1017/S0305004121000219

Author

Bianchi, Andrea. / Braid groups, mapping class groups and their homology with twisted coefficients. In: Mathematical Proceedings of the Cambridge Philosophical Society. 2022 ; Vol. 172, No. 2. pp. 249-266.

Bibtex

@article{d34c592890bd4a97a71529f255b6e508,
title = "Braid groups, mapping class groups and their homology with twisted coefficients",
abstract = "We consider the Birman-Hilden inclusion φ:Br2g+1→Γg,1 of the braid group into the mapping class group of an orientable surface with boundary, and prove that φ is stably trivial in homology with twisted coefficients in the symplectic representation H1(Σg,1) of the mapping class group; this generalises a result of Song and Tillmann regarding homology with constant coefficients. Furthermore we show that the stable homology of the braid group with coefficients in φ∗(H1(Σg,1)) has only 4-torsion.",
author = "Andrea Bianchi",
year = "2022",
doi = "10.1017/S0305004121000219",
language = "English",
volume = "172",
pages = "249--266",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Braid groups, mapping class groups and their homology with twisted coefficients

AU - Bianchi, Andrea

PY - 2022

Y1 - 2022

N2 - We consider the Birman-Hilden inclusion φ:Br2g+1→Γg,1 of the braid group into the mapping class group of an orientable surface with boundary, and prove that φ is stably trivial in homology with twisted coefficients in the symplectic representation H1(Σg,1) of the mapping class group; this generalises a result of Song and Tillmann regarding homology with constant coefficients. Furthermore we show that the stable homology of the braid group with coefficients in φ∗(H1(Σg,1)) has only 4-torsion.

AB - We consider the Birman-Hilden inclusion φ:Br2g+1→Γg,1 of the braid group into the mapping class group of an orientable surface with boundary, and prove that φ is stably trivial in homology with twisted coefficients in the symplectic representation H1(Σg,1) of the mapping class group; this generalises a result of Song and Tillmann regarding homology with constant coefficients. Furthermore we show that the stable homology of the braid group with coefficients in φ∗(H1(Σg,1)) has only 4-torsion.

U2 - 10.1017/S0305004121000219

DO - 10.1017/S0305004121000219

M3 - Journal article

VL - 172

SP - 249

EP - 266

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -

ID: 291831498