Polyfolds, cobordisms, and the strong Weinstein conjecture

Abstract

We prove the strong Weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres.

Diffeomorphism type of symplectic fillings of unit cotangent bundles

“…As shown in [6,Theorem 3.4], the contact manifold (M, ξ) is a convex boundary of the symplectic manifold D Z , ω Z | DZ , so the latter constitutes a symplectic filling. Alternatively, one may appeal to [19,Remark 3.3], which gives an elementary argument. In order to apply either reference in the present setting, one needs to appeal to Cieliebak's splitting theorem for subcritical Stein manifolds [4,Section 14.4].…”

Polyfolds and Fredholm Theory

“…The abstract theory has been applied in [28] as part of the general construction of SFT. In [51] it was used to address the Weinstein conjecture in higher dimensions. An extensive study of the case with boundary and corners is contained in [29,30].…”

Fillings and fittings of unit cotangent bundles of odd-dimensional spheres

“…Cap constructions were used in [5,9] to verify instances of the Weinstein conjecture, and in [2] for classifications of subcritical fillings. In the critical case too, symplectic caps are essential.…”