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arXiv · 1802.05479

Voros symbols as cluster coordinates

Dylan G. L. Allegretti
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Abstract

We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock-Goncharov coordinates of framed $PGL_2(\mathbb{C})$-local systems on a marked bordered surface. Using this result, we show that these Borel sums can be meromorphically continued to any point of $\mathbb{C}^*$, and we prove an asymptotic property of the monodromy map introduced in collaboration with Tom Bridgeland.

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Dylan G. L. Allegretti. 2018-02-15. Voros symbols as cluster coordinates. https://doi.org/10.1112/topo.12106

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