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Three-Manifold Quantum Invariants and Mock Theta Functions
- Source :
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. Volume 378, Issue 2163 (2019)
- Publication Year :
- 2019
-
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.<br />Comment: 19 pages
Details
- Database :
- arXiv
- Journal :
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. Volume 378, Issue 2163 (2019)
- Publication Type :
- Report
- Accession number :
- edsarx.1912.07997
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1098/rsta.2018.0439