Automorphisms of the Torelli complex for the one-holed genus two surface

Details Automorphisms of the Torelli complex for the one-holed genus two surface Automorphisms of the Torelli complex for the one-holed genus two surface

2010-09-03

arxiv.org/abs/1009.0568v2

Mathematics

Group Theory

19 pages, 4 figures

Scientific paper

Let S be a connected, compact and orientable surface of genus two with one boundary component. We study automorphisms of the Torelli complex for S and describe any isomorphism between finite index subgroups of the Torelli group for S. More generally, we study superinjective maps from the Torelli complex for S into itself and show that any finite index subgroup of the Torelli group for S is co-Hopfian.

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