Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II

dc.creatorIrmak, Elmas
dc.date2003-11-23
dc.date2003-12-29
dc.date.accessioned2026-07-07T05:03:11Z
dc.date.available2026-07-07T05:03:11Z
dc.descriptionLet R be a compact, connected, orientable surface of genus g with p boundary components. Let C(R) be the complex of curves on R and Mod_R^* be the extended mapping class group of R. Suppose that either g = 2 and p > 1 or g > 2 and p >= 0. We prove that a simplicial map lambda from C(R) to C(R) is superinjective if and only if it is induced by a homeomorphism of R. As a corollary, we prove that if K is a finite index subgroup of Mod_R^* and f is an injective homomorphism from K to Mod_R^*, then f is induced by a homeomorphism of R and f has a unique extension to an automorphism of Mod_R^*. This extends the author's previous results about closed connected orientable surfaces of genus at least 3, to the surface R.
dc.description37 pages, 19 figures; The proof for surfaces of genus two with at least two boundary components is added
dc.identifierhttps://arxiv.org/abs/math/0311407
dc.identifierhttp://arxiv.org/abs/math/0311407
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69314
dc.subjectGeometric Topology
dc.subject57M99 (Primary), 20F38 (Secondary)
dc.titleSuperinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II
dc.typetext

Files

Collections