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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.

category: reference

Revised on January 28, 2009 21:20:17 by Urs Schreiber (134.100.222.156)