On the symplectic fillings of standard real projective spaces

Abstract

We prove, in a geometric way, that the standard contact structure on the real projective space of dimension $2n-1$ is not Liouville fillable for $n\ge 3$ and odd. We also prove that, for all $n$, semipositive fillings of those contact structures are simply connected. Finally we give yet another proof of the Eliashberg-Floer-McDuff theorem on the diffeomorphism type of the symplectically aspherical fillings of the standard contact structure on the $(2n-1)$-dimensional sphere.

16 pages; several improvements in the exposition

References in corpus (1)

• $({\mathbb{RP}}^{2n-1},{\xi }_{std})$ is not exactly fillable for $n\ne 2^k$

Cited by in corpus (2)

• First Steps in Twisted Rabinowitz-Floer Homology
• On fillings of contact links of quotient singularities