Communications in Number Theory and Physics
Volume 13 (2019)
Integrality of the LMOV invariants for framed unknot
Pages: 81 – 100
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.
Received 18 March 2018
Accepted 25 August 2018
Published 29 April 2019