3D Topological Models and Heegaard Splitting I: Partition Function

Abstract

The aim of this article is twofold: firstly, we show how to recover the smooth Deligne-Beilinson cohomology groups from a Heegaard splitting of a closed oriented smooth 3-manifold by extending the usual \tch-de Rham construction; secondly, thanks to the above and still relying on a Heegaard splitting, we explain how to compute the partition functions of the $U(1)$ Chern-Simons and BF theories.

References in corpus (5)

• Path-integral invariants in abelian Chern-Simons theory
• Abelian BF theory and Turaev-Viro invariant
• A reciprocity formula from abelian BF and Turaev-Viro theories
• Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas
• Flat connections in three-manifolds and classical Chern-Simons invariant

Cited by in corpus (1)

• 3D Topological Models and Heegaard Splitting II: Pontryagin duality and Observables