A Morse-Bott approach to contact homology

By Frederick J. Bourgeois III. 2002

310 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/62a4649ae096b1736caa44fa0942bf36c873a69e

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Citations in the corpus

Bordered Heegaard Floer homology (2008, methodology): “Let N be a graded k-module, equipped with a map δ1 : N → (A⊗N)[1], satisfying the compatibility condition that (μ2 ⊗ IN) ◦ (IA ⊗ δ1) ◦ δ1 + (μ1 ⊗ IN) ◦ δ1 : N → A⊗N vanishes.”
Relative asymptotic behavior of pseudoholomorphic half‐cylinders (2007, background): “We remark that in practice the exponential convergence to a periodic orbit that we require in the definition of asymptotically cylindrical is usually a consequence of the cylinder ũ satisfying a finite energy condition and the periodic orbit P being either nondegenerate or Morse-Bott (see [7, 6, 2, ”
Bilinearised Legendrian contact homology and the augmentation category (2012, methodology): “Similarly to [2], one can consider the Morse-Bott approach to Legendrian contact homology using a Morse-Bott generic compatible almost complex structure J on R×M .”
Amoebas of Algebraic Varieties and Tropical Geometry (2004, methodology): “cycle contained in an aﬃne plane in R3. Conjecturally all regular curves are limits of the corresponding complex amoebas. Hopefully the technique developed in the Symplectic Field Theory, see [9] and [7] can help to verify this conjecture. Let us formulate a tropical enumerative tropical problem in ”
Cluster homology: An overview of the construction and results (2006, result): “Other instances are the work of Schwarz [15] as well as Piunikhin-Salamon-Schwarz [13] and more recently Bourgeois [3].”
A biased view of symplectic cohomology (2007, background): “The preparation of these notes was partially funded by NSF grant DMS-0405516.”
An exact sequence for contact- and symplectic homology (2007, methodology): “22 in [7] with arguments for gluing holomorphic curves along nondegenerate Reeb orbits in SFT ([3] and [6, Proposition 5]), we produce a Floer trajectory in Ŵ τ for H ∞,δ, for τ > 0 large enough and δ > 0 small enough.”
Reeb orbits and the minimal discrepancy of an isolated singularity (2014, methodology): “on 4.4. A Morse Bott family of Reeb orbits of (C,α) of period Tis a closed submanifold B⊂ Cwhere Bis a union of closed Reeb orbits of period T, and if φt: C→ C is the Reeb ﬂow then Ker(DφT)|B= TB(see [Bou02]). The families of critical points that we will be dealing with in Section 5.2 will be manifo”
Tropical Geometry and its applications (2006, unknown): “The proof in the general case (though in a somewhat different language) is contained in [2] (cf.”
Lagrangian spheres, symplectic surfaces and the symplectic mapping class group (2010, methodology): “Since each Reeb orbit is in a 2 dimensional manifold and has CZ index 2, following the computation on [22; 9], we have”
A hierarchy of local symplectic filling obstructions for contact $3$-manifolds (2010, background): “ss A 0= −[u0] ∈ H2(M,ρ −γ ). The perturbation from Jto J′ creates some additional J′-holomorphic cylinders which arise from gradient ﬂow lines along the Morse-Bott families of orbits, as described in [Bou02]. 60 CHRIS WENDL uσ,τ T1 T2 γe 1 γe 1 γh 1 γe 2 γh 2 v+ 1 v− 1 v+ 2 v− 2 u0 Figure 19. The pe”
Rational symplectic field theory over Z2 for exact Lagrangian cobordisms (2006, background): “We note that an end of an exact cobordism is good if the corresponding (±∞)boundary is a sphere of any dimension endowed with a contact form which is sufficiently close to the standard contact form (see [1, 15]).”
Contact homology and virtual fundamental cycles (2015, methodology): “ntly know whether these results hold for the deﬁnition of contact homology we give here. Note that for the above calculations, it would be very convenient to use Morse–Bott techniques as in Bourgeois [Bou02]. Our methods can probably be generalized to the Morse– Bott setting. It should bepossible to”