A cubical model for path spaces in d-simplicial complexes (Q411814)
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scientific article; zbMATH DE number 6029117
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A cubical model for path spaces in d-simplicial complexes |
scientific article; zbMATH DE number 6029117 |
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A cubical model for path spaces in d-simplicial complexes (English)
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30 April 2012
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The notion of \(d\)-simplicial complex (a directed version of the notion of simplicial complex) is introduced. The author constructs a precubical model of the space of directed paths between two points of a finite \(d\)-simplicial complex. It is proved that if the \(d\)-simplicial complex is without directed loops, the geometric realization of this precubical model is homotopy equivalent to the space of paths between the same points in the geometric realization of the \(d\)-simplicial complex.
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directed space
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simplicial complex
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path space
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