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

Abstract

We prove that $({\mathbb{RP}}^{2n-1},{\xi }_{std})$ is not exactly fillable for any $n\ne 2^k$ and there exist strongly fillable but not exactly fillable contact manifolds for all dimension $\ge 5$.

Revised version with more self-contained expository and more detailed proofs, comments welcome!

Cited by in corpus (4)

• On the symplectic fillings of standard real projective spaces
• On filings of $\partial (V\times \mathbb{D})$
• On fillings of contact links of quotient singularities
• A landscape of contact manifolds via rational SFT