Khovanov module and the detection of unlinks

By M. Hedden, Yi Ni. 2012

69 citations recorded by the source corpus.

We study a module structure on Khovanov homology, which we show is natural under the Ozsvath–Szabo spectral sequence to the Floer homology of the branched double cover. As an application, we show that this module structure detects trivial links. A key ingredient of our proof is that the Λ∗H_1–module structure on Heegaard Floer homology detects S^1 × S^2 connected summands.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/567820348a071c841c8a89815ff97a26557f3627

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Functoriality of colored link homologies (2017, background): “For example, Hedden–Ni [19] have shown that they enable Khovanov homology to detect unlinks (it was later proven that the module structure is determined by the bigraded vector space structure in the case of the unlink [4]), see also Wu [54] for a related result for the triply-graded homology.”
Annular Khovanov homology and knotted Schur–Weyl representations (2015, background): “Temporarily forgetting the data of the basepoint X, recall [21, 22, 16] that we have an action of”
A combinatorial spanning tree model for knot Floer homology (2011, background): “However, the similarities between 1Using [19], Hedden and Ni showed that the total rank of K̃h detects the 2-component unlink [12] and that K̃h, equipped with some additional algebraic structure, detects all unlinks [13].”