Advances in Theoretical and Mathematical Physics

Volume 9 (2005)

Number 2

Abelian homotopy Dijkgraaf-Witten theory

Pages: 321 – 353



Søren K. Hansen

Johannes K. Slingerland

Paul R. Turner


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.

Published 1 January 2005