The following preprint is available from my web page:


M. Grandis
Cubical cospans and higher cobordisms (Cospans in Algebraic Topology,  
III)
Dip. Mat. Univ. Genova, Preprint 559 (2007).

http://www.dima.unige.it/~grandis/wCub3.pdf
http://www.dima.unige.it/~grandis/wCub3.ps

Abstract. After two papers on weak cubical categories and collarable  
cospans, respectively, we put things together and construct a weak  
cubical category of cubical collared cospans of topological spaces.  
We also build a second structure, called a quasi cubical category,  
formed of arbitrary cubical cospans concatenated by homotopy  
pushouts. This structure, simpler but weaker, has 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.

The previous two papers of the same series are available at:

http://www.tac.mta.ca/tac/volumes/18/12/18-12.dvi   (ps, pdf)
http://www.dima.unige.it/~grandis/wCub2.pdf


Marco Grandis

Dipartimento di Matematica
Università di Genova
Via Dodecaneso, 35
16146 Genova
Italy

e-mail: grandis@dima.unige.it
tel: +39 010 353 6805
http://www.dima.unige.it/~grandis/