Gram determinant of planar curves

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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.
20 pages, 13 figures

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Geometric Topology, 57M, 05A

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http://salesiana.dossiersoluciones.com/handle/123456789/227035

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.4649
 http://arxiv.org/abs/0810.4649

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arXiv