Knot lattice homology in L-spaces

Peter Ozsváth; András Stipsicz; Zoltán Szabó

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arXiv · 1207.3889

Knot lattice homology in L-spaces

Peter Ozsváth·András Stipsicz·Zoltán Szabó

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Abstract

We show that the knot lattice homology of a knot in an L-space is equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring Z/2Z [U]). Suppose that G is a negative definite plumbing tree which contains a vertex w such that G-w is a union of rational graphs. Using the identification of knot homologies we show that for such graphs the lattice homology HF(G)$ is isomorphic to the Heegaard Floer homology HF^-(Y_G) of the corresponding rational homology sphere Y_G.

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BibTeX RIS

Peter Ozsváth, András Stipsicz, Zoltán Szabó. 2012-07-17. Knot lattice homology in L-spaces. https://arxiv.org/abs/1207.3889

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