Contact surgeries and the transverse invariant in knot Floer homology
Peter Ozsvath, Andras Stipsicz
TL;DR
This paper investigates how the transverse invariant in knot Floer homology behaves under contact (+1)-surgery, providing a new computational approach and applying it to show certain twist knots are not transversely simple.
Contribution
It introduces a method to analyze the transverse invariant's naturality under contact (+1)-surgery and applies it to classify twist knots.
Findings
Eliashberg-Chekanov twist knots E_n are not transversely simple for odd n > 3.
The study offers a new calculational tool for the transverse invariant.
Insights into the behavior of the transverse invariant under contact surgeries.
Abstract
We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov twist knots E_n are not transversely simple for n odd and n>3.
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