Gram determinant of planar curves

Jozef H. Przytycki; Xiaoqi Zhu

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arXiv · 0810.4649

Gram determinant of planar curves

Jozef H. Przytycki·Xiaoqi Zhu

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Abstract

We investigate the Gram determinant of the bilinear form based on curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on $n-1$ curves divides the determinant based on $n$ curves. Motivated by the work on Gram determinants based on curves in a disk and curves in an annulus (Temperley-Lieb algebra of type $A$ and $B$, respectively), we calculate several examples of the Gram determinant based on curves in a disk with two holes and advance conjectures on the complete factorization of Gram determinants.

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BibTeX RIS

Jozef H. Przytycki, Xiaoqi Zhu. 2008-10-25. Gram determinant of planar curves. https://arxiv.org/abs/0810.4649

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