English

A lower bound on tunnel number degeneration

Geometric Topology 2016-07-20 v1

Abstract

We prove a theorem which bounds Heegaard genus from below under special kinds of toroidal amalgamations of 33-manifolds. As a consequence, we conclude t(K1#K2)max{t(K1),t(K2)}t(K_1\# K_2)\geq \max\{t(K_1),t(K_2)\} for any pair of knots K1,K2S3K_1,K_2\subset S^3, where t(K)t(K) denotes the tunnel number of KK.

Keywords

Cite

@article{arxiv.1407.3554,
  title  = {A lower bound on tunnel number degeneration},
  author = {Trent Schirmer},
  journal= {arXiv preprint arXiv:1407.3554},
  year   = {2016}
}

Comments

22 pages, 6 figures

R2 v1 2026-06-22T05:03:08.725Z