Gram determinant of planar curves

Details Gram determinant of planar curves Gram determinant of planar curves

2008-10-25

arxiv.org/abs/0810.4649v1

Mathematics

Geometric Topology

20 pages, 13 figures

Scientific paper

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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