Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661545 | Topology and its Applications | 2006 | 32 Pages |
Abstract
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 be the extended mapping class group of R. Suppose that either g=2 and p⩾2 or g⩾3 and p⩾0. We prove that a simplicial map 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 and is an injective homomorphism, then f is induced by a homeomorphism of R and f has a unique extension to an automorphism of . This extends the author's previous results about closed connected orientable surfaces of genus at least 3, to the surface R.
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Mathematics
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