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- W2040959938 abstract "This paper combines the proofs and the results given by the author in [13; 8] about simplicial maps of complexes of curves on nonorientable surfaces. The complex of curves of a compact, connected, orientable surface was defined as an abstract simplicial complex by Harvey in [7] as follows: The vertex set consists of isotopy classes of nontrivial simple closed curves, where nontrivial means it does not bound a disk and it is not isotopic to a boundary component of the surface. Vertices form a simplex if they can be represented by pairwise disjoint simple closed curves on the surface. For a compact, connected, nonorientable surface N , the complex of curves C.N / is defined similarly where a simple closed curve is called nontrivial if it does not bound a disk or a Mobius band, and it is not isotopic to a boundary component of the surface. Simplicial maps such as automorphisms, superinjective simplicial maps and injective simplicial maps of the complexes of curves on surfaces are studied to get information about the mapping class groups of these surfaces. The mapping class group is defined as the group of isotopy classes of all self-homeomorphisms of the surface." @default.
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- W2040959938 date "2014-03-21" @default.
- W2040959938 modified "2023-09-26" @default.
- W2040959938 title "On simplicial maps of the complexes of curves of nonorientable surfaces" @default.
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- W2040959938 doi "https://doi.org/10.2140/agt.2014.14.1153" @default.
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