Non-realizability of the Torelli group as area-preserving homeomorphisms

Author: 

Chen, L
Markovic, V

Publication Date: 

28 June 2020

Journal: 

Journal of the London Mathematical Society

Last Updated: 

2021-08-23T02:09:07.72+01:00

DOI: 

10.1112/jlms.12340

abstract: 

Nielsen realization problem for the mapping class group Mod(๐‘†๐‘”) asks whether the natural projection ๐‘๐‘”:Homeo+(๐‘†๐‘”)โ†’Mod(๐‘†๐‘”) has a section. While all the previous results use torsion elements in an essential way, in this paper, we focus on the much more difficult problem of realization of torsionโ€free subgroups of Mod(๐‘†๐‘”) . The main result of this paper is that the Torelli group has no realization inside the areaโ€preserving homeomorphisms.

Symplectic id: 

1117196

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article