Cospans in Algebraic Topology
A series of articles by Marco Grandis on describing extended cobordisms in terms of multi-cospans in Top
I, Higher cospans and weak cubical categories (pdf)
II, Collared cospans, cohomotopy and TQFT (pdf)
III: Cubical cospans and higher cobordisms (arXiv)
Some of the crucial ideas appearing here are
a notion of cubical multi-cospans in some category;
the observation that extended cobordisms should be modeled by such multi-cospans (in particular in Top);
the observation that such cospans naturally map into spans by homming them into target objects, and that such spans can be linearized such as to yield FQFTs.
- (Grandis seems not to mention (?) the fact that groupoidification makes this interpretation of spans as linear maps very natural)
the relevance of evaluating functors which preserve (homotopy) pushouts on (multi)-cospans.
Revised on January 28, 2009 21:20:17
by Urs Schreiber