JournalsjemsVol. 18, No. 8pp. 1651–1674

Periodic knots and Heegaard Floer correction terms

  • Stanislav Jabuka

    University of Nevada Reno, USA
  • Swatee Naik

    University of Nevada Reno, USA
Periodic knots and Heegaard Floer correction terms cover
Download PDF

Abstract

We derive new obstructions to periodicity of classical knots by employing the Heegaard Floer correction terms of the finite cyclic branched covers of the knots. Applying our results to 2-fold covers, we demonstrate through numerous examples that our obstructions are successful where many existing periodicity obstructions fail.

A combination of previously known periodicity obstructions and the results presented here leads to a nearly complete (with the exception of a single knot) classification of alternating, periodic, 12-crossing knots with odd prime periods. For the case of alternating knots with 13, 14 and 15 crossings, we give a complete list of all periodic knots with odd prime periods q>3q > 3.

Cite this article

Stanislav Jabuka, Swatee Naik, Periodic knots and Heegaard Floer correction terms. J. Eur. Math. Soc. 18 (2016), no. 8, pp. 1651–1674

DOI 10.4171/JEMS/624