Holomorphic triangle invariants and the topology of symplectic four-manifolds

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

99 citations recorded by the source corpus.

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing result for the invariants of symplectic four-manifolds, which leads to new proofs of the indecomposability theorem for symplectic four-manifolds and the symplectic Thom conjecture. As a new application, we generalize the indecomposability theorem to splittings of four-manifolds along a certain class of three-manifolds obtained by plumbings of spheres. This leads to restrictions on the topology of Stein fillings of such three-manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/29d9e3822bd69d242534effff3a58a13472a3f26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Peter S. Ozsv'ath
2. Zolt'an Szab'o
3. M. Hedden
4. Robert Lipshitz
5. A. Stipsicz
6. O. Plamenevskaya
7. John A. Baldwin
8. Ciprian Manolescu

In Mathematical Physics

1. Peter S. Ozsv'ath
2. Zolt'an Szab'o
3. M. Hedden
4. Robert Lipshitz
5. John A. Baldwin
6. Ciprian Manolescu
7. A. Stipsicz
8. Jacob Rasmussen

Citations in the corpus

• Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary (2001, unknown): “More calculations will be given in [23].”
• Contact Structures with Distinct Heegaard Floer Invariants (2003, background): “Proposition 2.”
• Holomorphic disks and genus bounds (2003, methodology): “(The non-vanishing result from [34] is analogous to a non-vanishing theorem for the Seiberg–Witten invariants of symplectic manifolds proved by Taubes, cf.”
• A cylindrical reformulation of Heegaard Floer homology (2005, background): “Geometry & Topology 10 (2006) 955–1096 955 arXiv version: fonts, pagination and layout may vary from GT published version”
• GRADED ROOTS AND SINGULARITIES (2007, unknown): “1) [52].”
• Heegaard Floer homology and integer surgeries on links (2010, unknown): “3 in [18] says that (1 − UN )HF(Y, u) = 0 for some N ≥ 1.”