Brieskorn manifolds in contact topology

Abstract

In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving exotic contact structures, invariants and orderability. The main tool for the required computations is a version of the Morse-Bott spectral sequence. We provide a proof for the particular version that is useful for us.

arXiv commentCorrected typos and mistakes. Added an appendix with a proof of the Morse-Bott spectral sequence for both the equivariant and non-equivariant theory, added another appendix with proofs of the invariance properties of the mean Euler characteristic

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• Géométrie de contact: de la dimension trois vers les dimensions supérieures
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• Geometry of contact transformations and domains: orderability versus squeezing
• Compact Stein surfaces with boundary as branched covers of $\B^4$
• $S^1$-equivariant symplectic homology and linearized contact homology
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• Periodic Symplectic Cohomologies
• Contact manifolds with symplectomorphic symplectizations

Cited by in corpus (30)

• Symplectic homology and the Eilenberg-Steenrod axioms
• Koszul duality patterns in Floer theory
• Liouville hypersurfaces and connect sum cobordisms
• A Boothby-Wang theorem for Besse contact manifolds
• A Log PSS morphism with applications to Lagrangian embeddings
• Lagrangian sections on mirrors of toric Calabi-Yau 3-folds
• Vanishing of Symplectic Homology and Obstruction to Flexible Fillability
• Automatic transversality in contact homology II: filtrations and computations
• Symplectic fillings of asymptotically dynamically convex manifolds I
• Symplectic fillings of asymptotically dynamically convex manifolds II--$k$-dilations
• Existence and classification of overtwisted contact structures in all dimensions
• Homological mirror symmetry for Milnor fibers of simple singularities
• Volume growth in the component of fibered twists
• Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
• Two closed orbits for non-degenerate Reeb flows
• Equivariant wrapped Floer homology and symmetric periodic Reeb orbits
• Intrinsic mirror symmetry and categorical crepant resolutions
• Selective symplectic homology with applications to contact non-squeezing
• Planarity in higher-dimensional contact manifolds
• Reeb orbits and the minimal discrepancy of an isolated singularity
• Viterbo's transfer morphism for symplectomorphisms
• Exotic symplectomorphisms and contact circle actions
• Index bounded relative symplectic cohomology
• Reeb Dynamics of the Link of the $A_n$ Singularity
• Perfect Reeb flows and action-index relations
• A landscape of contact manifolds via rational SFT
• Stein domains with exotic contact boundaries
• A computation of the ring structure in wrapped Floer homology
• Symplectic cohomology of quasihomogeneous $c{A}_n$ singularities
• Connected sums of Brieskorn contact $5$-spheres