Hiroyuki Fuji, Masahide Manabe, “Some Generalizations of Mirzakhani's Recursion and Masur–Veech Volumes via Topological Recursions”, SIGMA, 2024, Volume 20,043, 86 pp.

This article is cited in 2 papers

Some Generalizations of Mirzakhani's Recursion and Masur–Veech Volumes via Topological Recursions

Hiroyuki Fuji^a, Masahide Manabe^bc

^a Center for Mathematical and Data Sciences and Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
^b Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
^c Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Abstract: Via Andersen–Borot–Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur–Veech polynomials was uncovered. The purpose of this article is to explore generalizations of Mirzakhani's recursion based on physical two-dimensional gravity models related to the Jackiw–Teitelboim gravity and to provide an introduction to various realizations of topological recursion. For generalized Mirzakhani's recursions involving a Masur–Veech type twist, we derive Virasoro constraints and cut-and-join equations, and also show some computations of generalized volumes for the physical two-dimensional gravity models.

Keywords: topological recursion, Weil–Petersson volume, Masur–Veech volume, quantum Airy structure, Jackiw–Teitelboim gravity.

MSC: 81T45, 14D21, 14N10

Received: April 4, 2023; in final form May 9, 2024; Published online May 27, 2024

Language: English

DOI: 10.3842/SIGMA.2024.043