Contact Structures with Distinct Heegaard Floer Invariants

By O. Plamenevskaya. 2003

88 citations recorded by the source corpus.

We prove that the contact structures on Y= dX induced by non-homotopic Stein structures on the 4-manifold X have distinct Heegaard Floer invariants.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a08b933934c69be22248d11d984c8f2f0baac941

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In Computational Theory and Mathematics

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Citations in the corpus

Planar open books and Floer homology (2005, background): “For the induced Spin structure s(J) on X the condition c1(X, J) 6= 0 readily implies s(J) 6= s(J), hence by [14] we get that ξ and ξ are not isotopic, in fact, according to [26] we also know that c(ξ) 6= c(ξ).”
Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “D Y has an open book decomposition whose monodromy is a product of positive Dehn twists around curves corresponding to the vanishing cycles; this open book is compatible with the contact structure by Plamenevskaya [25].”
Strongly fillable contact 3-manifolds without Stein fillings (2005, background): “Theorem 3.4 [ 20, Theorem 4 ] Let W be a smooth compact 4–manifold with boundary Y = @W . Let J1, J2 be two Stein structures on W that induce Spinc–structures s1, s2 on W and contact structures �1, �2 on Y . We puncture W and regard it as a cobordism from −Y to S3. Suppose that s1|Y is isotopic to s”
Tight contact structures on some small Seifert fibered 3-manifolds (2005, background): “As proved by Plamenevskaya [33], tight contact structures distinguished in this way have different contact Ozsváth–Szabó invariants.”
Ozsváth-Szabó invariants and fillability of contact structures (2004, background): “ relating HF+ and HFdand the isomorphism between HFd d(Y) and HFd−d(−Y) it is easy to show that HFd(−Σ(2,3,6n+5)) = (Z/2Z)n+1 (+2) ⊕(Z/2Z)2 (+1) . The degree of c(ξ) is +1 because d3(η i) = −3 2 . By [25], Section 4 HFd (+1)(−Σ(2,3,6n+5)) is freely generated by the elements c(η i) for i ∈ P∗ n . Pro”
Heegaard Floer homology and genus one, one‐boundary component open books (2008, unknown): “Then (W, J̄) is a Stein-filling of ξT ,φ , and Plamenevskaya proves in [41] that c(ξT ,φ) = c(ξT ,φ).”