A general state-sum construction of 2-dimensional topological quantum field theories with defects

作者：Kamau Devers Gathoni; Jardine Gail; Yetter David^*

来源：Journal of Knot Theory and Its Ramifications, 2017, 26(4): 1750014.

DOI：10.1142/S0218216517500146

• Topological quantum field theory
• defects
• flag-like triangulation
• state-sum

We derive a general state sum construction for 2D topological quantum field theories (TQFTs) with source defects on oriented curves, extending the state-sum construction from special symmetric Frobenius algebra for 2D TQFTs without defects (cf. Lauda and Pfeiffer [State-sum construction of two-dimensional open-closed topological quantum field theories, J. Knot Theory Ramifications 16 (2007) 1121-1163, doi:10.1142/S0218216507005 725]). From the extended Pachner moves (Crane and Yet-ter [Moves on filtered PL manifolds and stratified PL spaces, arXiv: 1404.3142]), we derive equations that we subsequently translate into string diagrams so that we can easily observe their properties. As in Dougherty, Park and Yetter [On 2-dimensional Dijkgraaf-Witten theory with defects, to appear in J. Knots Theory Ramifications], we require that triangulations be flaglike, meaning that each simplex of the triangulation is either disjoint from the defect curve, or intersects it in a closed face, and that the extended Pachner moves preserve flaglikeness.

• 出版日期2017-4