Corpus ID: 235899364

Cylindrical contact homology of links of simple singularities

@inproceedings{Digiosia2021CylindricalCH,
  title={Cylindrical contact homology of links of simple singularities},
  author={Leo Digiosia},
  year={2021}
}
We compute the cylindrical contact homology of the links of the simple singularities. These manifolds are contactomorphic to S3/G for finite subgroups G ⊂ SU(2). We perturb the degenerate contact form on S3/G with a Morse function, invariant under the corresponding H ⊂ SO(3) action on S2, to achieve nondegeneracy up to an action threshold. The cylindrical contact homology is recovered by taking a direct limit of the action filtered homology groups. The ranks of this homology are given in terms… Expand

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SHOWING 1-10 OF 27 REFERENCES
Cylindrical contact homology for dynamically convex contact forms in three dimensions
We show that for dynamically convex contact forms in three dimensions, the cylindrical contact homology differential d can be defined by directly counting holomorphic cylinders for a generic almostExpand
Cylindrical contact homology of 3-dimensional Brieskorn manifolds
Cylindrical contact homology is a comparatively simple incarnation of symplectic field theory whose existence and invariance under suitable hypotheses was recently established by Hutchings andExpand
Automatic transversality in contact homology II: filtrations and computations
  • J. Nelson
  • Mathematics
  • Proceedings of the London Mathematical Society
  • 2019
This paper is the sequel to the previous paper [Ne15] which showed that sufficient regularity exists to define cylindrical contact homology in dimension 3 for dynamically separated contact forms, aExpand
$S^1$-equivariant symplectic homology and linearized contact homology
We present three equivalent definitions of $S^1$-equivariant symplectic homology. We show that, using rational coefficients, the positive part of $S^1$-equivariant symplectic homology is isomorphicExpand
Automatic transversality in contact homology I: regularity
This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments failExpand
Embedded contact homology of prequantization bundles
The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. WeExpand
Automatic transversality and orbifolds of punctured holomorphic curves in dimension four
We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results ofExpand
Orbifold Morse–Smale–Witten complexes
Given a Morse–Smale function on an effective orientable orbifold, we construct its Morse–Smale–Witten complex. We show that critical points of a certain type have to be discarded to build a complexExpand
Compactness results in Symplectic Field Theory
This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in (4). We prove compactness results for moduli spaces of holomorphic curves arising in SymplecticExpand
Reeb dynamics of the link of the An singularity
The link of the $A_n$ singularity, $L_{A_n} \subset \mathbb{C}^3$ admits a natural contact structure $\xi_0$ coming from the set of complex tangencies. The canonical contact form $\alpha_0$Expand
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