#### Volume 25, issue 6 (2021)

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

### Zhengyi Zhou

Geometry & Topology 25 (2021) 3013–3052
##### Abstract

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

##### Keywords
exact filling, symplectic cohomology, quotient singularity
##### Mathematical Subject Classification 2010
Primary: 53D05, 53D10, 53D42, 57R17
Secondary: 14B05