Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Modular Knots, Automorphic Forms, and the Rademacher Symbols for Triangle Groups
Toshiki Matsusaka (Nagoya University)
Abstract:
In a celebrated paper “Knots and dynamics”, Étienne Ghys proved that the linking numbers of modular knots and the missing trefoil in

coincide with the values of a highly ubiquitous function called the Rademacher symbol for
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. In this talk, we replace
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by the triangle group
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for any coprime pair $(p,q)$ of integers with

. We invoke the theory of harmonic Maass forms for
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to introduce the notion of the Rademacher symbol and provide several characterizations. Among other things, we generalize Ghys’s theorem for modular knots around any missing torus knot in

and in a lens space. This is joint work with Jun Ueki (Tokyo Denki University).
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