Notes on simplicial BF theory

Abstract

In this work we discuss the construction of "simplicial BF theory", the field theory with finite-dimensional space of fields, associated to a triangulated manifold, that is in a sense equivalent to topological BF theory on the manifold (with infinite-dimensional space of fields). This is done in framework of simplicial program - program of constructing discrete topological field theories. We also discuss the relation of these constructions to homotopy algebra.

References in corpus (4)

• Deformation quantization of Poisson manifolds, I
• Lie theory for nilpotent L-infinity algebras
• A geometric discretisation scheme applied to the Abelian Chern-Simons theory
• R-torsion and linking numbers from simplicial abelian gauge theories

Cited by in corpus (6)

• Poisson sigma model on the sphere
• Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
• Unimodular homotopy algebras and Chern-Simons theory
• Unimodular L-infinity algebras
• Trace Anomaly in Geometric Discretization
• 2D and 3D topological field theories for generalized complex geometry