Geometric subgroups of surface braid groups

Luis Paris; Dale Rolfsen

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 2, page 417-472
  • ISSN: 0373-0956

Abstract

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Let M be a surface, let N be a subsurface, and let n ≤ m be two positive integers. The inclusion of N in M gives rise to a homomorphism from the braid group B n N with n strings on N to the braid group B m M with m strings on M . We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of π 1 N in π 1 M . Then we calculate the commensurator, the normalizer and the centralizer of B n N in B m M for large surface braid groups.

How to cite

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Paris, Luis, and Rolfsen, Dale. "Geometric subgroups of surface braid groups." Annales de l'institut Fourier 49.2 (1999): 417-472. <http://eudml.org/doc/75344>.

@article{Paris1999,
abstract = {Let $M$ be a surface, let $N$ be a subsurface, and let $n\le m$ be two positive integers. The inclusion of $N$ in $M$ gives rise to a homomorphism from the braid group $B_nN$ with $n$ strings on $N$ to the braid group $B_mM$ with $m$ strings on $M$. We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of $\pi _1 N$ in $\pi _1M$. Then we calculate the commensurator, the normalizer and the centralizer of $B_nN$ in $B_mM$ for large surface braid groups.},
author = {Paris, Luis, Rolfsen, Dale},
journal = {Annales de l'institut Fourier},
keywords = {braid groups; surfaces; commensurators; normalizers; centralizers; subgroups; fundamental groups},
language = {eng},
number = {2},
pages = {417-472},
publisher = {Association des Annales de l'Institut Fourier},
title = {Geometric subgroups of surface braid groups},
url = {http://eudml.org/doc/75344},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Paris, Luis
AU - Rolfsen, Dale
TI - Geometric subgroups of surface braid groups
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 2
SP - 417
EP - 472
AB - Let $M$ be a surface, let $N$ be a subsurface, and let $n\le m$ be two positive integers. The inclusion of $N$ in $M$ gives rise to a homomorphism from the braid group $B_nN$ with $n$ strings on $N$ to the braid group $B_mM$ with $m$ strings on $M$. We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of $\pi _1 N$ in $\pi _1M$. Then we calculate the commensurator, the normalizer and the centralizer of $B_nN$ in $B_mM$ for large surface braid groups.
LA - eng
KW - braid groups; surfaces; commensurators; normalizers; centralizers; subgroups; fundamental groups
UR - http://eudml.org/doc/75344
ER -

References

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