Advances in Theoretical and Mathematical Physics
Volume 9 (2005)
Abelian homotopy Dijkgraaf-Witten theory
Pages: 321 – 353
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.
2010 Mathematics Subject Classification
Primary 53Cxx. Secondary 55Pxx, 57Rxx, 58Jxx, 81T45.