Cubical cospans and higher cobordisms (Cospans in algebraic topology, III)

Details Cubical cospans and higher cobordisms (Cospans in algebraic topology, III) Cubical cospans and higher cobordisms (Cospans in algebraic topology, III)

2008-06-14

arxiv.org/abs/0806.2359v1

Mathematics

Algebraic Topology

To be published in "Journal of Homotopy and Related Structures"

Scientific paper

After two papers on weak cubical categories and {\it collarable} cospans, respectively, we put things together and construct a {\it weak} cubical category of cubical {\it collared} cospans of topological spaces. We also build a second structure, called a {\it quasi} cubical category, formed of arbitrary cubical cospans concatenated by homotopy pushouts. This structure, simpler but weaker, has {\it lax} identities. It contains a similar framework for cobordisms of manifolds with corners and could therefore be the basis to extend the study of TQFT's of Part II to higher cubical degree.

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