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.

Corrected 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

References in corpus (4)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Functors and Computations in Floer homology with Applications Part II
• Symplectic cohomology and Viterbo's theorem
• Periodic Symplectic Cohomologies

Cited by in corpus (29)

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