English

Voros symbols as cluster coordinates

Classical Analysis and ODEs 2020-01-22 v3 High Energy Physics - Theory Geometric Topology

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 PGL2(C)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 C\mathbb{C}^*, and we prove an asymptotic property of the monodromy map introduced in collaboration with Tom Bridgeland.

Cite

@article{arxiv.1802.05479,
  title  = {Voros symbols as cluster coordinates},
  author = {Dylan G. L. Allegretti},
  journal= {arXiv preprint arXiv:1802.05479},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T00:23:18.830Z