Communications in Number Theory and Physics

Volume 13 (2019)

Number 1

Integrality of the LMOV invariants for framed unknot

Pages: 81 – 100

DOI: https://dx.doi.org/10.4310/CNTP.2019.v13.n1.a3

Authors

Wei Luo (Department of Mathematics and Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China)

Shengmao Zhu (Department of Mathematics and Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China)

Abstract

The Labastida–Marinõ–Ooguri–Vafa (LMOV) invariants are the open string BPS invariants which are expected to be integers based on the string duality conjecture from $M$-theory. Several explicit formulae of LMOV invariants for framed unknot have been obtained in the literature. In this paper, we present a unified method to deal with the integrality of such explicit formulae. Furthermore, we also prove the integrality of certain LMOV invariants for framed unknot in higher genera.

Full Text (PDF format)

Received 18 March 2018

Accepted 25 August 2018

Published 29 April 2019