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Non-realizability of the pure braid group as area-preserving homeomorphisms

Chen, Lei (2021) Non-realizability of the pure braid group as area-preserving homeomorphisms. Ergodic Theory and Dynamical Systems, 41 (7). pp. 1988-1999. ISSN 0143-3857. doi:10.1017/etds.2020.37. https://resolver.caltech.edu/CaltechAUTHORS:20210610-103120284

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Abstract

Let Homeo₊(D²_n) be the group of orientation-preserving homeomorphisms of D² fixing the boundary pointwise and n marked points as a set. The Nielsen realization problem for the braid group asks whether the natural projection p_n : Homeo₊(D²_n) → B_n : = π₀(Homeo₊(D²_n)) has a section over subgroups of B_n. All of the previous methods use either torsion or Thurston stability, which do not apply to the pure braid group P B_n, the subgroup of B_n that fixes n marked points pointwise. In this paper, we show that the pure braid group has no realization inside the area-preserving homeomorphisms using rotation numbers.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/etds.2020.37DOIArticle
https://arxiv.org/abs/2002.10918arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Lei0000-0002-5941-7914
Additional Information:© The Author(s) 2020. Published by Cambridge University Press. Received 23 February 2020 and accepted in revised form 8 April 2020. Published online by Cambridge University Press: 11 June 2020. The author would like to thank Vlad Markovic for helpful discussions and the anonymous referee for help with the writing.
Subject Keywords:group actions; low-dimensional dynamics; topological dynamics
Issue or Number:7
Classification Code:2020 Mathematics Subject Classification: 57K20 (Primary); 37E30, 37C25 (Secondary)
DOI:10.1017/etds.2020.37
Record Number:CaltechAUTHORS:20210610-103120284
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210610-103120284
Official Citation:Chen, L. (2021). Non-realizability of the pure braid group as area-preserving homeomorphisms. Ergodic Theory and Dynamical Systems, 41(7), 1988-1999. doi:10.1017/etds.2020.37
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109467
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Jun 2021 17:49
Last Modified:10 Jun 2021 17:49

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