Contact homology and homotopy groups of the space of contact structures
By Frederick J. Bourgeois III. 2004
56 citations recorded by the source corpus.
Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact manifolds and higher order homotopy groups.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f33151ebd7aff5981bf26334b56cfc423e398ffb
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In Geometry and Topology
- Chris Wendl
- Klaus Niederkruger
- Baptiste Chantraine
- Tam'as K'alm'an
- L. Polterovich
- Y. Eliashberg
- Sang Seon Kim
- Patrick Massot
In Mathematical Physics
- Chris Wendl
- Klaus Niederkruger
- Baptiste Chantraine
- Y. Eliashberg
- Sang Seon Kim
- Patrick Massot
- Tam'as K'alm'an
- L. Polterovich
Citations in the corpus
- Contact homology and one parameter families of Legendrian knots (2004, background): “ll defined up to homotopy, therefore its action is well defined). In particular, a non-trivial monodromy implies the non-triviality of the fibration. As already demonstrated by Seidel [26] and Bourgeois [4], the continuation (monodromy) map can prove non-triviality theorems, in a way analogous to the a”
- Erratum to “Geometry of contact transformations and domains: orderability versus squeezing” (2005, background): “The proof of this statement is scattered in the literature for various classes of framed Hamiltonian structures (see eg [31; 14; 5]).”
- Lagrangian concordance of Legendrian knots (2006, methodology): “Following Bourgeois [5] we see that a Lagrangian cylinder between two Legendrian knots could be used to define a map between the algebras CH(K+) and CH(K−) (see Ekholm, Etnyre and Sullivan [6]).”
- Weak and strong fillability of higher dimensional contact manifolds (2011, methodology): “Transversality for these curves can therefore be achieved via a generic perturbation of the almost complex structure, using the standard result of Dragnev [12] (see also the appendix of [5]).”