A Generalization of the Gram determinant of type A

Rhea Palak Bakshi; Dionne Ibarra; Sujoy Mukherjee; Józef H. Przytycki

doi:10.1016/j.topol.2021.107663

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arXiv · 1905.07834

A Generalization of the Gram determinant of type A

Rhea Palak Bakshi·Dionne Ibarra·Sujoy Mukherjee·Józef H. Przytycki

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Abstract

The Gram determinant of type $A$ was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type $A$ by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determinant. We conclude the paper by discussing Chen's conjecture about the Gram determinant of type $Mb$ evaluated in the Klein bottle.

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Rhea Palak Bakshi, Dionne Ibarra, Sujoy Mukherjee, Józef H. Przytycki. 2019-05-20. A Generalization of the Gram determinant of type A. https://doi.org/10.1016/j.topol.2021.107663

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