Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 4 (2014), 2445-2474.
Low-dimensional linear representations of the mapping class group of a nonorientable surface
Suppose that is a homomorphism from the mapping class group of a nonorientable surface of genus with boundary components to . We prove that if , and , then factors through the abelianization of , which is for and for . If , and , then either has finite image (of order at most two if ), or it is conjugate to one of four “homological representations”. As an application we prove that for and , every homomorphism factors through the abelianization of .
Algebr. Geom. Topol., Volume 14, Number 4 (2014), 2445-2474.
Received: 6 May 2013
Revised: 17 January 2014
Accepted: 31 January 2014
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F38: Other groups related to topology or analysis
Secondary: 57N05: Topology of $E^2$ , 2-manifolds
Szepietowski, Błażej. Low-dimensional linear representations of the mapping class group of a nonorientable surface. Algebr. Geom. Topol. 14 (2014), no. 4, 2445--2474. doi:10.2140/agt.2014.14.2445. https://projecteuclid.org/euclid.agt/1513715969