Spin Modular Categories

Anna Beliakova; Christian Blanchet; Eva Contreras

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arXiv · 1411.4232

Spin Modular Categories

Anna Beliakova·Christian Blanchet·Eva Contreras

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Abstract

Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or generalized spin and complex spin structures. A crucial role in our construction is played by objects which are invertible under tensor product. All known examples of cohomological or spin type refinements of the Witten-Reshetikhin-Turaev 3-manifold invariants are special cases of our construction. In addition, we establish a splitting formula for the refined invariants, generalizing the well-known product decomposition of quantum invariants into projective ones and those determined by the linking matrix.

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Anna Beliakova, Christian Blanchet, Eva Contreras. 2014-11-16. Spin Modular Categories. https://arxiv.org/abs/1411.4232

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