- journal article metadata
European Mathematical Society Publishing House
2017-08-25 23:45:01
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2017
3
Spin modular categories
Anna
Beliakova
Universität Zürich, Switzerland
Christian
Blanchet
Université Paris-Diderot, France
Eva
Contreras
University of California, Berkeley, USA
TQFT, modular category, quantum invariant, spin structure
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to de fine re finements 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 re nements of the Witten–Reshetikhin–Turaev 3-manifold invariants are special cases of our construction. In addition, we establish a splitting formula for the re fined invariants, generalizing the well-known product decomposition of quantum invariants into projective ones and those determined by the linking matrix.
Manifolds and cell complexes
Quantum theory
459
504
10.4171/QT/95
http://www.ems-ph.org/doi/10.4171/QT/95