arXiv subjects

Hong-Chuan Gan

Publications and source records attributed to Hong-Chuan Gan.

2 recordsLinked to original sources

arXiv2022

Bipyramid Volume, Mahler Measure and Some $\mathbb{Z}^2$-periodic Links

Champanerkar, Kofman and Lalín conjectured an inequality between bipyramid volume of links and Mahler measure of associated dimer models induced from alternating links on torus. Hyperbolic volume and Mahler measure can be related for isoradial graphs, which allows us to confirm the conjecture for two examples. By exploiting a connection between perfect matchings of dimer models and spanning trees on lattices, five more examples are calculated.

math.GT↗

arXiv2020

Alternating links with totally geodesic checkerboard surfaces

We prove that alternating links with two totally geodesic checkerboard surfaces are three links with projection the 1-skeleton of the octahedron, the cuboctahedron and the icosidodecahedron. We also characterize these links as right-angled completely realisable links and show that all hyperbolic weaving knots with two exceptions have both checkerboard surfaces not totally geodesic.

math.GT↗