Handle attaching in symplectic homology and the Chord Conjecture

By Kai Cieliebak. 2002

122 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1ee90de9a892de54bf6acf963ecf4c743c4ce760

How researchers see this paper

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

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Altering symplectic manifolds by homologous recombination (2010, background): “This is still almost symplectomorphic to X , and by [12] it satisfies”
Topological quantum field theory structure on symplectic cohomology (2010, methodology): “If ∂M⊂X is displaceable then RFH∗(∂M⊂X)=0 by Cieliebak-Frauenfelder [11].”
Brieskorn manifolds in contact topology (2013, methodology): “It is known that symplectic homology does not change under subcritical handle attachment due to work of Cieliebak [16, Theorem 1.11].”
Symplectic homology as Hochschild homology (2006, unknown): “ar X iv :m at h/ 06 09 03 7v 4 [ m at h. SG ] 9 A pr 2 00 8 SYMPLECTIC HOMOLOGY AS HOCHSCHILD HOMOLOGY PAUL SEIDEL”
Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces (2007, methodology): “Our construction is modelled on those of Cieliebak, Floer, Hofer and Viterbo [6, 7, 13, 28].”
The positive equivariant symplectic homology as an invariant for some contact manifolds (2015, background): “24 ([8]) Let (αt)t∈[0,1] be a smooth family of contact forms on a closed manifold M of dimension 2n − 1.”
An exact sequence for contact- and symplectic homology (2007, background): “The symplectic homology groups SH∗(W ) of the subcritical Stein domain W vanish for the trivial homotopy class [9,25], and the tautological long exact sequence (5) implies SH+ k−(n−3)(W ) Hk+2(W, ∂W ), k ∈ Z.”
Symplectic homology and the Eilenberg-Steenrod axioms (2015, methodology): “The vanishing of SH∗(W,∂ W ) is proved in [24] with arbitrary coefficients as a consequence of the following fact: for each degree i there exists bi > 0 such that SH (a,b) i (W,∂ W ) = 0 for any a < 0 and b ≥ bi.”
Effect of Legendrian surgery (2009, methodology): “According to a theorem of K. Cieliebak, see [11], any subcritical Weinstein manifoldX of dimension 2n is symplectomorphic to a productX′ × R2, where X′ is a Weinstein manifold of dimension 2n − 2.”
Contact geometry of the restricted three‐body problem (2010, background): “By Cieliebak’s [4] computation of the symplectic homology of a boundary-connected sum, see also McLean [14, Theorem 2.20] for an improvement concerning the ring structure, we know ) .”
Sectorial descent for wrapped Fukaya categories (2018, background): “recovers the folklore result that subcritical handle attachment does not change the wrapped Fukaya category (the closest results in the literature concern the closed string analogue symplectic cohomology [14]; see also [19]).”
Floer theory for negative line bundles via Gromov–Witten invariants (2011, background): “This phenomenon is apparent in the literature, where known computations involve showing vanishing results by indirect grading/action tricks (for example, for X = C and generally X = subcritical Stein manifold [7]).”
The Künneth formula in Floer homology for manifolds with restricted contact type boundary (2004, background): “ed from below plurisubharmonic Morse functions with only a ﬁnite number of critical points, all of index strictly less than 1 2 dimR Mc [El]. They satisfy the SAWC as proved by Viterbo [V]. Cieliebak [C1] has proved that their Floer homology actually vanishes. We can recoverthis through Theorem A by”
Rabinowitz Floer homology and symplectic homology (2009, methodology): “Since W is subcritical we have SH∗(W ) = 0 [7], so that the unit vanishes in SH∗(W ).”
Lefschetz fibrations and symplectic homology (2007, background): “This was already done by Cieliebak in [7] but without taking into account the ring structure.”