• Corpus ID: 239049413

Floer homology, twist coefficients, and capping off

@inproceedings{Reinoso2021FloerHT,
  title={Floer homology, twist coefficients, and capping off},
  author={Braeden Reinoso},
  year={2021}
}
For an open book decomposition (S, φ), the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy φ twists the surface S near each boundary component. In general, the twist coefficients do not behave nicely under the operation of capping off a boundary component. The goal of this paper is to use Heegaard Floer homology to constrain the behavior of the fractional Dehn twist coefficients after capping off. We also use our results about fractional Dehn… 

Figures from this paper

References

SHOWING 1-10 OF 17 REFERENCES
Floer Homology and Fractional Dehn Twists
We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a
Fractional Dehn twists in knot theory and contact topology
Fractional Dehn twists give a measure of the difference between the relative isotopy class of a homeomorphism of a bordered surface and the Thurston representative of its free isotopy class. We show
Essential open book foliations and fractional Dehn twist coefficient
We introduce essential open book foliations by refining open book foliations, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed
The twisted Floer homology of torus bundles
Given a torus bundle $Y$ over the circle and a cohomology class $[\omega]\in H^2(Y;\mathbb{Z})$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted
On the contact class in Heegaard Floer homology
We present an alternate description of the Ozsvath-Szabo contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M,\xi) has an adapted open book
Capping off open books and the Ozsvath-Szabo contact invariant
If (S, φ) is an open book with disconnected binding, then we can form a new open book (S′, φ′) by capping off one of the boundary components of S with a disk. LetMS,φ denote the 3-manifold with open
Holomorphic disks and three-manifold invariants: Properties and applications
In [27], we introduced Floer homology theories HF - (Y,s), HF∞(Y,s), HF + (Y, t), HF(Y,s),and HF red (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spiny structures s ∈ Spin
Admissible transverse surgery does not preserve tightness
We produce the first examples of closed, tight contact 3-manifolds which become overtwisted after performing admissible transverse surgeries. Along the way, we clarify the relationship between
Non-Exact Symplectic Cobordisms Between Contact 3-Manifolds
We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in
Tight contact structures via admissible transverse surgery
  • J. Conway
  • Mathematics
    Journal of Knot Theory and Its Ramifications
  • 2019
We investigate the line between tight and overtwisted for surgeries on fibered transverse knots in contact 3-manifolds. When the contact structure [Formula: see text] is supported by the fibered knot
...
1
2
...