Contact Surgery Numbers of Projective Spaces

Article Type

Research Article

Publication Title

Mediterranean Journal of Mathematics

Abstract

We classify all contact projective spaces with contact surgery number one. In particular, this implies that there exist infinitely many non-isotopic contact structures on the real projective 3-space which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere. Large parts of our proofs deal with a detailed analysis of Gompf’s Γ-invariant of tangential 2-plane fields on 3-manifolds. From our main result, we also deduce that the Γ-invariant of a tangential 2-plane field on the real projective 3-space only depends on its d3-invariant.

DOI

10.1007/s00009-025-02936-w

Publication Date

9-1-2025

Link to Full Text

Share

COinS