Abstract
We construct a version of Dijkgraaf–Witten theory based on a compact abelian Lie group within the formalism of Turaev’s homotopy quantum field theory. As an application we show that the $2+1$-dimensional theory based on $\rm U(1)$ classifies lens spaces up to homotopy type.
Citation
Søren K. Hansen. Johannes K. Slingerland. Paul R. Turner. "Abelian homotopy Dijkgraaf-Witten theory." Adv. Theor. Math. Phys. 9 (2) 321 - 353, April 2005.
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