Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the homology of the commutator subgroup of the pure braid group


Author: Andrea Bianchi
Journal: Proc. Amer. Math. Soc. 149 (2021), 2387-2401
MSC (2020): Primary 20F36, 55R20, 55R35, 55R80, 16S34, 20C07
DOI: https://doi.org/10.1090/proc/15404
Published electronically: March 29, 2021
MathSciNet review: 4246792
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the homology of $[P_{n},P_{n}]$, the commutator subgroup of the pure braid group on $n$ strands, and show that $H_l([P_{n},P_{n}])$ contains a free abelian group of infinite rank for all $1\leq l\leq n-2$. As a consequence we determine the cohomological dimension of $[P_{n},P_{n}]$: for $n\geq 2$ we have $\mathrm {cd}([P_{n},P_{n}])=n-2$.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 20F36, 55R20, 55R35, 55R80, 16S34, 20C07

Retrieve articles in all journals with MSC (2020): 20F36, 55R20, 55R35, 55R80, 16S34, 20C07


Additional Information

Andrea Bianchi
Affiliation: Mathematics Institute, University of Bonn, Endenicher Allee 60, Bonn, Germany
Address at time of publication: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, Denmark
MR Author ID: 1324567
Email: anbi@math.ku.dk

Keywords: Pure braid group, commutator subgroup, cohomological dimension.
Received by editor(s): March 17, 2020
Received by editor(s) in revised form: October 19, 2020
Published electronically: March 29, 2021
Additional Notes: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2047/1, 390685813)
Communicated by: Julie Bergner
Article copyright: © Copyright 2021 American Mathematical Society