The periodic Floer homology of a Dehn twist.

By Michael Hutchings, Michael C. Sullivan. 2004

61 citations recorded by the source corpus.

The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits, and whose differential counts certain embedded pseudoholomorphic curves in R cross the mapping torus. It is conjectured to recover the Seiberg-Witten Floer homology of the mapping torus for most spin-c structures, and is related to a variant of contact homology. In this paper we compute the periodic Floer homology of some Dehn twists. AMS Classification 57R58; 53D40, 57R50

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/490f26d606f1df8167ad1a0f64cb555d9acf940d

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Rounding corners of polygons and the embedded contact homology of T 3 (2004, methodology): “mplexes by ECH^ ∗(T 3,λ n;Γ,H2(T 2)) ≃ He ∗(2πn;Γ), (112) ECH∗(T3,λn;Γ) ≃ H∗(2πn;Γ). (113) 86 Proof. This is similar to the computation of the periodic Floer homology of a Dehn twist on a cylinder in [10], because the mapping torus ﬂow for a negative Dehn twist on a cylinder is isomorphic to the Ree”
Heegaard Floer homology and genus one, one‐boundary component open books (2008, background): “For instance, when φ is the identity, Hutchings and Sullivan show in [14] that the embedded contact homology of M̂T,φ ∼= T 3 agrees with its Heegaard and Seiberg-Witten Floer homologies up to shifts in grading, evidence for the conjecture that these three Floer theories are equivalent despite their ”
Symplectic Floer homology of area-preserving surface diffeomorphisms (2008, methodology): “PFH has been computed for a single Dehn twist and certain other cases [21], but no pseudo-Anosov cases are known for g > 1.”
Lecture Notes on Embedded Contact Homology (2013, methodology): “The definition of PFH is given in [21, 27], and it shown in [38] that PFH agrees with Seiberg-Witten Floer homology.”
The embedded contact homology index revisited (2008, background): “5 Stable Hamiltonian structures Embedded contact homology is very similar to the periodic Floer homology (PFH) of mapping tori considered in [11, 12].”
HF=HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology (2010, methodology): “This relationship also has antecedents in the theorem of the second and the third authors proved in [13] that equates Hutchings’s periodic Floer homology for fibered 3-manifolds (see [3]) with a version of Seiberg–Witten Floer cohomology.”
Gluing pseudoholomorphic curves along branched covered cylinders II (2007, methodology): “rem 1.13 in a special (but nontrivial) case to prove that the ECH diﬀerential ∂satisﬁes ∂2 = 0. Essentially the same argument shows that the diﬀerential in the periodic Floer homology of mapping tori [11] also has square zero. After some combinatorial preliminaries in §7.1, the deﬁnition of the ECH ”