A normal generating set for the Torelli group of a non-orientable closed surface

2014/12/06 by Susumu Hirose, Hirose, Susumu, Ryoma Kobayashi +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1412.2222

Abstract

For a closed surface S, its Torelli group I(S) is the subgroup of the mapping class group of S consisting of elements acting trivially on H₁(S;ℤ). When S is orientable, a generating set for I(S) is known. In this paper, we give a normal generating set of I(N_g) for g≥4, where N_g is a genus-g non-orientable closed surface.

Citations

• Curves on 2-manifolds and isotopies

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