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Macquarie University  Department of Mathematics

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Workshop on Categorical Methods in Algebra, Geometry and Mathematical Physics

Satellite to the StreetFest conference in honour of Ross Street's sixtieth birthday

July 18-21 2005, Australian National University, Canberra

Wed, 20 July:  10:30 - 11:10

Homotopy Quantum Field Theories with background a 2-type, formal maps and gerbes.
Porter, Timothy (University of Wales, Bangor)

\thanks{Joint work with Vladimir Turaev.}
Homotopy quantum field theories can be used to study `$d$-manifolds with background $B$'. These were introduced by Turaev in 2000 but generalise ideas of Segal on Conformal QFTs. Turaev classified HQFTs for $d = 1$ when the background was a $K(G,1)$. Brightwell and Turner examined the case when $B$ is a $K(A,2)$ and Rodrigues showed that for any dimension $d$ the HQFTs only depended on the $(d+1)$-type of $B$.

There is an obvious question. If we have an algebraic model for the $2$-type of $B$, can we extend Turaev and Brightwell--Turner to classify all such HQFTs? VT and TP have done this in terms of the crossed-module model for the 2-type and a combinatorial notion of formal map. A slightly surprising spin-off is an interpretation of these HQFTs as classifying gerbes of a suitable type, generalising $G$-torsors.

Typeset PDF of this abstract.