English

On framings of links in 3-manifolds

Geometric Topology 2023-04-17 v2 Algebraic Topology

Abstract

We show that the only way of changing the framing of a link by ambient isotopy in an oriented 33-manifold is when the manifold has a properly embedded non-separating S2S^2. This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCullough's work on the mapping class groups of 33-manifolds. We also relate our results to the theory of skein modules.

Keywords

Cite

@article{arxiv.2001.07782,
  title  = {On framings of links in 3-manifolds},
  author = {Rhea Palak Bakshi and Dionne Ibarra and Gabriel Montoya-Vega and Józef H. Przytycki and Deborah Weeks},
  journal= {arXiv preprint arXiv:2001.07782},
  year   = {2023}
}

Comments

12 pages, 9 figures