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arXiv · 1912.07997

Three-Manifold Quantum Invariants and Mock Theta Functions

Miranda C. N. Cheng·Francesca Ferrari·Gabriele Sgroi
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Abstract

Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding we highlight a new area where mock modular forms start to play an important role, namely the study of three-manifold invariants. For a certain class of Seifert three-manifolds, we describe a conjecture on the mock modular properties of a recently proposed quantum invariant. As an illustration, we include concrete computations for a specific three-manifold, the Brieskorn sphere $\Sigma(2,3,7)$. This note is partially based on the talk by the first author in the conference "Srinivasa Ramanujan: in celebration of the centenary of his election as FRS" held at the Royal Society in 2018.

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Miranda C. N. Cheng, Francesca Ferrari, Gabriele Sgroi. 2019-12-17. Three-Manifold Quantum Invariants and Mock Theta Functions. https://doi.org/10.1098/rsta.2018.0439

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