arXiv Analytics

Sign in

arXiv:1009.0568 [math.GR]AbstractReferencesReviewsResources

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

Yoshikata Kida, Saeko Yamagata

Published 2010-09-03, updated 2013-04-14Version 4

Let S be a connected, compact and orientable surface of genus two having exactly 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.

Comments: 28 pages, 21 figures. Proof was largely modified because some hexagons had been overlooked (v3), Figures added and exposition improved (v4)
Categories: math.GR, math.GT
Subjects: 20E36, 20F38
Related articles: Most relevant | Search more
arXiv:0909.4718 [math.GR] (Published 2009-09-25, updated 2011-04-12)
Automorphisms of the Torelli complex and the complex of separating curves
arXiv:0911.3923 [math.GR] (Published 2009-11-20, updated 2011-05-19)
The co-Hopfian property of the Johnson kernel and the Torelli group
arXiv:0802.0185 [math.GR] (Published 2008-02-01, updated 2008-11-04)
Free Groups in Lattices

Links

Toolbox