Preprint: Homotopical interpretation of globular complex by multipointed d-space

Preprint: Homotopical interpretation of globular complex by multipointed d-space

[Gaucher Philippe]

Dear All,

Here is a new preprint:

Title:
Homotopical interpretation of globular complex by multipointed d-space

Abstract:
Globular complexes were introduced by E. Goubault and the author to model
higher dimensional automata.  Globular complexes are topological spaces
equipped with a globular decomposition which is  the directed analogue of the
cellular decomposition of a CW-complex.  We prove that there exists a
combinatorial model category such that  the cellular objects are exactly the
globular complexes and such  that the homotopy category is equivalent to the
homotopy category of  flows.  The underlying category of this model category
is a variant  of M. Grandis' notion of d-space over a topological space
colimit  generated by simplices. This result enables us to understand the
relationship between the framework of flows and other works in  directed
algebraic topology using d-spaces. It also enables us to  prove that the
underlying homotopy type functor of flows can be  interpreted up to
equivalences of categories as the total left  derived functor of a left
Quillen adjoint.

Comment:
28 pages, 2 figures

Url:
http://www.pps.jussieu.fr/~gaucher/Mdtop.ps
http://www.pps.jussieu.fr/~gaucher/Mdtop.pdf