Contact surgeries and the transverse invariant in knot Floer homology

By Peter S. Ozsv'ath, A. Stipsicz. Journal of the Institute of Mathematics of Jussieu, 2008

65 citations recorded by the source corpus.

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 En are not transversely simple for n odd and n > 3.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/72b99c295bcdadc54f0745ca4cb46df66b8d2d42

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Citations in the corpus

Grid Homology for Knots and Links (2015, background): “(Indeed, [48] provides a complete classification of Legendrian/transverse twist knots; see also [163].”
Heegaard Floer homology and integer surgeries on links (2010, unknown): “The argument in [12] can also be applied to higher polygons, with the result that the chain homotopies between triangle and nearest point maps lift to chain homotopies between the respective hyperboxes.”
Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, background): “is the nth higher derivative on the spectral sequence associated to the ﬁltered chain complex CFK−(−Y,L)) is such a further structure, as it is exploited in [29]. In a slightly diﬀerent direction, in [31] two of the authors of the present paper have shown that the mapping class group MCG(Y,L) = Diﬀ+”