Injective Simplicial Maps of the Complex of Arcs on Nonorientable Surfaces
Injective Simplicial Maps of the Complex of Arcs on Nonorientable Surfaces
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DOI：
10.2140/agt.2009.9.2055
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发表时间：
2008-03
影响因子：
0.7
通讯作者：
Elmas Irmak
中科院分区：
文献类型：
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作者：
Elmas Irmak
我们证明了从紧的、连通的、非空边界的不可定向曲面的弧复到自身的每个内射单纯映射都是由该曲面的一个同胚导出的。证明了圆弧复形的自同构群与曲面的映射类群的商按其中心同构。57M99；20F38
We prove that each injective simplicial map from the complex of arcs of a compact, connected, nonorientable surface with nonempty boundary to itself is induced by a homeomorphism of the surface. We also prove that the automorphism group of the arc complex is isomorphic to the quotient of the mapping class group of the surface by its center. 57M99; 20F38