Superinjective simplicial maps of complexes of curves and injective homomorphisms of subgroups of mapping class groups
Superinjective simplicial maps of complexes of curves and injective homomorphisms of subgroups of mapping class groups
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DOI：
10.1016/j.top.2003.03.002
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发表时间：
2002-11
期刊：
影响因子：
--
通讯作者：
Elmas Irmak
中科院分区：
文献类型：
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作者：
Elmas Irmak
设S是亏格至少为3的闭连通可定向曲面，C（S）是S上的曲线复形，ModS是S的扩张映射类群.证明了单纯映射λ：C（S）→ C（S）保持不相交性（即如果α和β是C（S）中的两个顶点且i（α，β）<$0，则i（λ（α），λ（β））<$0）当且仅当它是由S的同胚诱导的.作为推论，我们证明了：如果K是ModS的有限指数子群，且f：K→ModS的自同构是单射同态，则f是由S的同胚诱导的，且f对ModS的自同构有唯一的扩张.
Let S be a closed, connected, orientable surface of genus at least 3, C (S) be the complex of curves on S and ModS∗be the extended mapping class group of S. We prove that a simplicial map, λ : C (S)→ C (S) , preserves nondisjointness (i.e. if α and β are two vertices in C (S) and i(α,β)≠0, then i(λ(α),λ(β))≠0) iff it is induced by a homeomorphism of S. As a corollary, we prove that if K is a finite index subgroup of ModS∗and f : K→ModS∗is an injective homomorphism, then f is induced by a homeomorphism of S and f has a unique extension to an automorphism of ModS∗.