Outdated Archival Version

These pages are not updated anymore. They reflect the state of 6 June 2010. For the current production of this journal, please refer to http://www.springer.com/mathematics/geometry/journal/40062.

Cubical cospans and higher cobordisms (Cospans in Algebraic Topology, III)

Marco Grandis

After two papers on weak cubical categories and {\it collarable} cospans, respectively, we putthings together and construct a {\it weak} cubical category of cubical {\it collared} cospans oftopological spaces. We also build a second structure, called a {\it quasi} cubical category, formed ofarbitrary 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 couldtherefore be the basis to extend the study of TQFT's of Part II to higher cubical degree.

Journal of Homotopy and Related Structures, Vol. 3(2008), No. 1, pp. 273-308