English

On non-isotopic spanning surfaces for a class of arborescent knots

Geometric Topology 2013-08-29 v2

Abstract

We use the methods of Hedden, Juhasz, and Sarkar to exhibit a set of arborescent knots that bound large numbers of non-isotopic minimal genus spanning surfaces. In particular, we describe a sequence of prime knots K_{n} which will bound at least 2^{2n-1} non-isotopic minimal spanning surfaces of genus n.

Keywords

Cite

@article{arxiv.1308.2899,
  title  = {On non-isotopic spanning surfaces for a class of arborescent knots},
  author = {Lawrence Roberts},
  journal= {arXiv preprint arXiv:1308.2899},
  year   = {2013}
}

Comments

15 pgs, 3 figures. Version 2 includes typographical and spelling corrections and an extension to the introduction which adds more information about previously known results for quantitative estimates on the number of spanning surfaces and a improved definition of "equivalence" as used in this paper