Knot Floer homology and integer surgeries

By Peter S. Ozsv'ath, Zolt'an Szab'o. 2004

217 citations recorded by the source corpus.

Let Y be a closed three-manifold with trivial first homology, and let K Y be a knot. We give a description of the Heegaard Floer homology of integer surgeries on Y along K in terms of the filtered homotopy type of the knot invariant for K . As an illustration of these techniques, we calculate the Heegaard Floer homology groups of non-trivial circle bundles over Riemann surfaces (with coefficients in Z=2Z). 57M27; 57M25

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/41b7a162038a3f9a01e298a64085588aab9f6270

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Citations in the corpus

Heegaard Floer homology as morphism spaces (2010, result): “This result can be compared with results from [14] or [18], which give alternate methods for computing the Heegaard Floer homology groups of 2-surgery on the left-handed trefoil.”
Topologically slice knots with nontrivial Alexander polynomial (2010, methodology): “The result of [43] that we will use to compute d(S3 q (K ), sm) requires that q ≥ 2g3(K ) − 1.”
Grid Homology for Knots and Links (2015, methodology): “Moreover, knot Floer homology is a useful device for computing the Heegaard Floer homology groups of three-manifolds obtained by Dehn surgery on K; see [181].”
Topologically slice knots of smooth concordance order two (2012, methodology): “We use the notation of [36, 37] and refer the reader there for more details.”
On Knot Floer Homology and Cabling: 2 (2008, background): “Quasipositive Seifert surfaces are those which can be obtained from parallel disks by attaching bands with a positive half twist (see Figure 1 of [11]).”
Heegaard Floer homology and integer surgeries on links (2010, unknown): “that appears in the knot surgery formula from [22].”
Cosmetic surgeries on knots in $S^3$ (2010, background): “As in [11], there are chain maps vk, hk : A + k → B .”
Lens space surgeries and L-space homology spheres (2007, background): “pping cone can be used to determine the maps induced by the corresponding surgery cobordism. (This is not explicitly stated in [24], but the analogous result for null-homologous knots may be found in [23], and the proof carries through without change.) The precise statement is as follows: for LENS S”
On the Khovanov and knot Floer homologies of quasi-alternating links (2007, background): “If a link L is homologically σ-thin over R = Z or F for a bigraded theory H (where H could denote either K̃h or ĤFK), then H(L) is completely determined by the signature σ of L and the Euler characteristic P (q) of H (the latter being either the Jones or a multiple of the Alexander polynomial).”
Knot Floer homology of Whitehead doubles (2006, methodology): “t HFd(S3 t (K),s i) is. (Recall that Ozsv´ath and Szab´o present a formula for HFd(S3 t (K),s i) in terms of the ﬁltered chain homotopy type of CFK∞(K). This is summarized below but see [33] and also [34, 35] for further details.) Using essentially the method of Ozsv´ath and Szab´o, we will prove th”
A connected sum formula for involutive Heegaard Floer homology (2016, background): “To state it, recall that the knot surgery formula in ordinary Heegaard Floer homology [25] makes use of a certain quotient complex A0 of the knot Floer complex CFK ∞(K).”
Involutive Heegaard Floer homology (2015, methodology): “The original references are [38] and [48]; here we use the notation from [44].”