On the Floer homology of plumbed three-manifolds

By Peter S. Ozsv'ath, Zolt'an Szab'o. 2002

256 citations recorded by the source corpus.

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres. These calculations can be used to determine also these groups for other three-manifolds, including the product of a circle with a genus two surface.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0552c2bc60622579b9ec787f41bb4faf9a4767d9

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Citations in the corpus

Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture (2013, methodology): “In particular, it would be interesting to compute our invariants for a larger class of plumbed 3-manifolds, as was done for Heegaard Floer homology in [45].”
Ozsváth-Szabó invariants and tight contact three-manifolds, II (2004, background): “ar X iv :m at h/ 05 05 49 3v 2 [ m at AMS Classification 57R17; 57R57 Keywords Ozsváth–Szabó invariants, L–spaces, taut foliations, transverse foliations, transverse contact structures, tight contact structures, planar contact structures”
The slice-ribbon conjecture for 3-stranded pretzel knots (2007, methodology): “ this obstruction, one needs to be able to calculate the correction terms d(Y K,s). While this is a hard problem in general, for the case at hand we can invoke a formula due to Ozsv´ath and Szab´o in [18]. We summarize their results below. Let Gbe a negative deﬁnite weighted graph (by which we mean ”
Knot Floer homology and integer surgeries (2004, methodology): “(Of course, ±1 surgeries on torus knots are Brieskorn spheres, and as such their Heegaard Floer homology groups can be calculated using the techniques of [13]; however, we find it instructive to sketch here the calculations using present methods.”
Tight contact structures on some small Seifert fibered 3-manifolds (2005, methodology): “Proof Since −Mp is the boundary of the plumbing P , we can apply the algorithm of [29] to determine its Ozsváth–Szabó homology groups.”
Lattice cohomology of normal surface singularities (2007, unknown): “Then, for any q, φ( q) has the form aφ( q)Uw( q)−n.”
On the Heegaard Floer homology of branched double-covers (2003, background): “This special class of three-manifolds is closed under connected sums and includes all lens spaces and, more generally, all Seifert fibered spaces with finite fundamental group; other examples are given in [19] and [16].”
Knot Floer homology, genus bounds, and mutation (2003, background): “It is easy to construct Seifert surfaces F for Cr,n with genus g(F ) = 2r−1, compare [3], see also Section 4.”
On the existence of tight contact structures on Seifert fibered 3-manifolds (2007, methodology): “In [31] Ozsv´ath and Szab´o prove the existence of an algorithm which computes HF ( Y ) assuming that Y is the boundary of a negative deﬁnite plumbing of a certain type.”
Floer simple manifolds and L-space intervals (2015, unknown): “In this section we use Ozsváth and Szabó’s mapping cone formula to prove Proposition 1.3 and to derive some basic facts about Floer simple manifolds.”
Monopoles and lens space surgeries (2003, methodology): “ is the following result, which follows quickly from [28]. Or, alternatively, using Theorem 2.4, one can adapt the proof of the corresponding result for Heegaard Floer homology (c.f. Corollary 1.4 of [34]), to the context of Seiberg-Witten monopoles. Theorem 8.9. If Y is a positively oriented Seifer”
Knot Floer homology and rational surgeries (2005, methodology): “It is interesting to compare the following construction with a construction of Némethi [12], see also [19].”
Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary (2001, background): “8 (see [24] for a more conceptual interpretation of these numbers).”