Twisting quasi-alternating links

By Abhijit Champanerkar, Ilya Kofman. 2007

74 citations recorded by the source corpus.

Quasi-alternating links are homologically thin for both Khovanov homology and knot Floer homology. We show that every quasi-alternating link gives rise to an infinite family of quasi-alternating links obtained by replacing a crossing with an alternating rational tangle. Consequently, we show that many pretzel links are quasi-alternating, and we determine the thickness of Khovanov homology for "most" pretzel links with arbitrarily many strands.

Subfields: Geometry and Topology, Neurology

View Paper: https://www.semanticscholar.org/paper/0bee1791230c1c94399d0907eb57eadc830ea19f

How researchers see this paper

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In Geometry and Topology

1. J. Greene
2. John A. Baldwin
3. Peter S. Ozsv'ath

In Neurology

1. J. Greene
2. John A. Baldwin

Citations in the corpus

• Homologically thin, non-quasi-alternating links (2009, methodology): “The family of links L(m,n), together with work of Champanerkar-Kofman [3] and Widmer [33], indicate some progress in extending Theorem 1.4 to the more general case of Montesinos links.”
• Heegaard Floer homology and genus one, one‐boundary component open books (2008, background): “Since this manuscript first appeared, Champanerkar and Kofman have shown in [ 3 ] (incorporating work of Josh Greene) that the remaining knots in this table are quasi-alternating, with the exception of 10140, which is not quasi-alternating by forthcoming work of Shumakovitch.”