TY - RPRT

T1 - Trace spaces in a pre-cubical complex

A1 - Raussen,Martin

AU - Raussen,Martin

PB - Department of Mathematical Sciences, Aalborg University

PY - 2008

Y1 - 2008

N2 - In directed algebraic topology, (spaces of) directed irreversible (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.

AB - In directed algebraic topology, (spaces of) directed irreversible (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.

BT - Trace spaces in a pre-cubical complex

T3 - Research Report Series

T3 - en_GB

ER -