Preprint available: Collared cospans, cohomotopy and TQFT

Preprint available: Collared cospans, cohomotopy and TQFT

[Marco Grandis]

The following preprint is available:

M. Grandis, Collared cospans, cohomotopy and TQFT (Cospans in
Algebraic Topology, II)
Dip. Mat. Univ. Genova, Preprint 555 (2007).

http://www.dima.unige.it/~grandis/wCub2.pdf
http://www.dima.unige.it/~grandis/wCub2.ps

Abstract. Topological cospans and their concatenation, by pushout,
appear in the theories of tangles, ribbons, cobordism, etc. Various
algebraic invariants have been introduced for their study, which it
would be interesting to link with the standard tools of Algebraic
Topology, (co)homotopy and (co)homology functors.

	Here we introduce collared cospans between topological spaces, as a
generalisation of the cospans which appear in the previous theories.
Their interest lies in the fact that their concatenation is realised
with homotopy pushouts. Therefore, cohomotopy functors induce
'functors' from collared cospans to spans of sets, providing - by
linearisation - topological quantum field theories (TQFT) on
manifolds and their cobordisms. Similarly, (co)homology and homotopy
functors take collared cospans to relations of abelian groups or (co)
spans of groups, yielding other 'algebraic' invariants.

	This is the second paper in a series devoted to the study of cospans
in Algebraic Topology. It is practically independent from the first,
which deals with higher cubical cospans in abstract categories. The
third article will proceed from both, studying cubical topological
cospans and their collared version.

____________

Marco Grandis