Strong Homotopy Types, Nerves and Collapses
نویسندگان
چکیده
منابع مشابه
Strong Homotopy Types, Nerves and Collapses
We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relati...
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We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relati...
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Two theorems are proved. One concerns coverings of a simplicial complex D by subcomplexes. It is shown that if every t-wise intersection of these subcomplexes is ðk t þ 1Þ-connected, then for jpk there are isomorphisms pjðDÞDpjðNÞ of homotopy groups of D and of the nerve N of the covering. The other concerns poset maps f : P-Q: It is shown that if all fibers f ðQpqÞ are kconnected, then f induc...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2011
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-011-9357-5