$({\mathbb{RP}}^{2n-1},{\xi }_{std})$ 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 $\ge 5$.

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

References in corpus (12)

• Compactness results in Symplectic Field Theory
• Geometry of contact transformations and domains: orderability versus squeezing
• An open string analogue of Viterbo functoriality
• Weak and strong fillability of higher dimensional contact manifolds
• Symplectic homology and the Eilenberg-Steenrod axioms
• Floer theory for negative line bundles via Gromov-Witten invariants
• The topology of Stein fillable manifolds in high dimensions I
• Strongly fillable contact 3-manifolds without Stein fillings
• Symplectic Homology of complements of smooth divisors
• Symplectic fillings of asymptotically dynamically convex manifolds I
• Exactly fillable contact structures without Stein fillings
• Quotient Theorems in Polyfold Theory and $S^1$-Equivariant Transversality

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