Geodesic
Witten–Reshetikhin–Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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Gukov–Pei–Putrov–Vafa constructed $ q $-series invariants called homological blocks in a physical way in order to categorify Witten–Reshetikhin–Turaev (WRT) invariants and conjectured that radial limits of homological blocks are WRT invariants. In this paper, we prove their conjecture for unimodular H-graphs. As a consequence, it turns out that the WRT invariants of H-graphs yield quantum modular forms of depth two and of weight one with the quantum set $ \mathbb{Q} $. In the course of the proof of our main theorem, we first write the invariants as finite sums of rational functions. We second carry out a systematic study of weighted Gauss sums in order to give new vanishing results for them. Combining these results, we finally prove that the above conjecture holds for H-graphs.
Keywords: quantum invariants, Witten–Reshetikhin–Turaev invariants, homological blocks, quantum modular forms, plumbed manifolds
Mots-clés : false theta funcitons, Gauss sums. 
@article{SIGMA_2022_18_a33,
     author = {Akihito Mori and Yuya Murakami},
     title = {Witten{\textendash}Reshetikhin{\textendash}Turaev {Invariants,} {Homological} {Blocks,} and {Quantum} {Modular} {Forms} {for~Unimodular} {Plumbing} {H-Graphs}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a33/}
}
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Akihito Mori; Yuya Murakami. Witten–Reshetikhin–Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a33/

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