Voros symbols as cluster coordinates
Abstract
We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as FockGoncharov 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.05479
 Bibcode:
 2018arXiv180205479A
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 High Energy Physics  Theory;
 Mathematics  Geometric Topology
 EPrint:
 46 pages. Version 2: Accepted for publication in Journal of Topology. Version 3: Clarifications added to Theorem 1.4 and its proof, superseding the published version