Non-Semisimple TQFT's and BPS -Series
Jul 29, 2021
71 pages
Published in:
- SIGMA 19 (2023) 010,
- SIGMA 19 (2023) 010
- Published: Mar 15, 2023
e-Print:
- 2107.14238 [math.GT]
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Abstract: (SIGMA)
We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows to study (and perhaps even to formulate) -series invariants labeled by spinc structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.- 3-manifold invariants
- knot invariants
- TQFT
- field theory: topological
- string model
- BPS
- quantum group
- spin
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