English

Clock Moves and Alexander Polynomial of Plane Graphs

Geometric Topology 2024-10-23 v2

Abstract

In this paper, we introduce a notion of clock moves for spanning trees in plane graphs. This enables us to develop a spanning tree model of an Alexander polynomial for a plane graph and prove the unimodal property of its associate coefficient sequence. In particular, this confirms the trapezoidal conjecture for planar singular knots and gives new insights to Fox's original conjecture on alternating knots.

Keywords

Cite

@article{arxiv.2410.16126,
  title  = {Clock Moves and Alexander Polynomial of Plane Graphs},
  author = {Wenbo Liao and Zhongtao Wu},
  journal= {arXiv preprint arXiv:2410.16126},
  year   = {2024}
}

Comments

29 pages, 27 figures