Trace spaces in a pre-cubical complex |
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Authors: | Martin Raussen |
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Affiliation: | Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg Øst, Denmark |
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Abstract: | In directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-paths are studied from a topological and from a categorical point of view. Motivated by models for concurrent computation, we study in this paper spaces of d-paths in a pre-cubical complex. Such paths are equipped with a natural arc length which moreover is shown to be invariant under directed homotopies. D-paths up to reparametrization (called traces) can thus be represented by arc length parametrized d-paths. Under weak additional conditions, it is shown that trace spaces in a pre-cubical complex are separable metric spaces which are locally contractible and locally compact. Moreover, they have the homotopy type of a CW-complex. |
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Keywords: | 54F65 55P10 54E35 54D30 54D65 68Q85 |
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