Category Archives: Contact homology

An alternate definition of local contact homology

This blog has been dormant for a while, but I have a backlog of topics to write about. The following is something I meant to write after the AIM workshop last December, where I suggested this in a discussion. 1. … Continue reading

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Is cylindrical contact homology defined with integer coefficients?

A confusing issue about cylindrical contact homology is whether it is defined with integer or rational coefficients. I would now like to try to clear this up once and for all. If I am not mistaken, the conclusions are the … Continue reading

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Lagrangian capacities and Ekeland-Hofer capacities

References for this post: [CM] K. Cieliebak and K. Mohnke, Punctured holomorphic curves and Lagrangian embeddings [HN] M. Hutchings and J. Nelson, Cylindrical contact homology for dynamically convex contact forms in three dimensions [BEYOND] M. Hutchings, Beyond ECH capacities [HL] … Continue reading

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Local contact homology with integer coefficients II

Continuing the previous post, I will now (1) outline how, for a nondegenerate contact form with no contractible Reeb orbits, one can define a version of contact homology with integer coefficients, analogously to the Bourgeois-Oancea definition of -equivariant symplectic homology … Continue reading

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Local contact homology with integer coefficients I

In a recent preprint, Bourgeois and Oancea define -equivariant symplectic homology, and show that if the transversality needed to define linearized contact homology holds, then these two homologies are isomorphic. For a while I was bothered by an apparent paradox. … Continue reading

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Problem with cylindrical cobordism maps fixed?

In a previous post, I discussed the problem of defining cylindrical contact homology for a contact three-manifold with no contractible Reeb orbits. (In that post I assumed for simplicity that there are no bad Reeb orbits, but I will allow … Continue reading

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An obstruction to cylindrical contact homology?

Last week I was at a very nice conference at IMPA, and one of the topics of informal discussion was to what extent cylindrical contact homology can be defined, in the absence of contractible Reeb orbits, but without using polyfolds. … Continue reading

Posted in Contact homology, Open questions | 7 Comments