Mathematics – Geometric Topology
Scientific paper
2003-11-23
Mathematics
Geometric Topology
37 pages, 19 figures; The proof for surfaces of genus two with at least two boundary components is added
Scientific paper
Let 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.
No associations
LandOfFree
Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-495575