English

The L^2 signature of torus knots

Geometric Topology 2010-06-28 v3 Algebraic Topology

Abstract

We find a formula for the L2 signature of a (p,q) torus knot, which is the integral of the omega-signatures over the unit circle. We then apply this to a theorem of Cochran-Orr-Teichner to prove that the n-twisted doubles of the unknot, for n not 0 or 2, are not slice. This is a new proof of the result first proved by Casson and Gordon.

Keywords

Cite

@article{arxiv.1001.1329,
  title  = {The L^2 signature of torus knots},
  author = {Julia Collins},
  journal= {arXiv preprint arXiv:1001.1329},
  year   = {2010}
}

Comments

11 pages, Version 2 contains a note explaining that the main theorem of the paper has already been proved in earlier work by Kirby and Melvin