A contact homotopy type
Abstract
Adapting the construction of global Kuranishi charts to the contact setting, we associate to any non-degenerate contact manifold a flow category based on Reeb orbits and moduli spaces of pseudo-holomorphic buildings. The construction lifts contact homology and is natural in the sense that to any exact symplectic cobordism we can associate a flow bimodule between the flow categories of its ends.
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