Genera of Vertex Operator Algebras and three dimensional Topological Quantum Field Theories

Abstract

The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements similar as known for quadratic forms are formulated. We further explain how extension problems for vertex operator algebras can bedescribed in terms of the associated modular braided tensor category.