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Spin modular categories


Beliakova, Anna; Blanchet, Christian; Contreras, Eva (2017). Spin modular categories. Quantum Topology, 8(3):459-504.

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 renements 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.

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 renements 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:31 March 2017
Deposited On:31 Oct 2017 14:59
Last Modified:19 Feb 2018 09:02
Publisher:EMS European Mathematical Society
ISSN:1664-073X
OA Status:Green
Publisher DOI:https://doi.org/10.4171/QT/95

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