2025/04/07 by Marc Kegel, Monika Yadav, Kegel, Marc +1 · 1 citation
Mathematics · #53D10 #53D35 #57K10 #57K33 #57R65 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2504.05032
openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.