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 Mtheory. 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.

中文翻译：

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框架 unknot 的 LMOV 不变量的完整性

摘要。Labastida-Marinõ-Ooguri-Vafa (LMOV) 不变量是开放字符串 BPS 不变量，根据 Mtheory 的字符串对偶性猜想，它预计是整数。在文献中已经获得了几个用于框架 unknot 的 LMOV 不变量的显式公式。在本文中，我们提出了一种统一的方法来处理这种显式公式的完整性。此外，我们还证明了某些 LMOV 不变量在高等属中框架 unknot 的完整性。