Realization of the mapping class group by homeomorphisms

Author: 

Markovic, V

Publication Date: 

1 June 2007

Journal: 

Inventiones Mathematicae

Last Updated: 

2021-01-10T14:19:37.89+00:00

Issue: 

3

Volume: 

168

DOI: 

10.1007/s00222-007-0039-0

page: 

523-566

abstract: 

In this paper, we show that the mapping class group of a closed surface can not be geometrically realized as a group of homeomorphisms of that surface. More precisely, let Pr: Homeo(M) → MC(M) denote the standard projection of the group of homeomorphisms to the mapping class group of a closed surface M of genus g>5. We show that there is no homomorphism ε: MC(M) → Homeo(M), such that Pr o ε is the identity. This answers a question by Thurston (see [11]). © Springer-Verlag 2007.

Symplectic id: 

1110007

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article