Three-manifold quantum invariants and mock theta functions
2019 ◽
Vol 378
(2163)
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pp. 20180439
Keyword(s):
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 Σ (2, 3, 7). This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.
2019 ◽
Vol 378
(2163)
◽
pp. 20180448
2012 ◽
Vol 29
(1-3)
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pp. 295-310
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Keyword(s):
Keyword(s):
2008 ◽
Vol 04
(06)
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pp. 1027-1042
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Keyword(s):
2009 ◽
Vol 145
(03)
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pp. 553-565
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2018 ◽
Vol 14
(07)
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pp. 1961-1981
2013 ◽
Vol 65
(3)
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pp. 781-805
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