Contact Surgery Numbers of Projective Spaces

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发表日期：

2025年8月22日

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Marc Kegel,
Monika Yadav

摘要

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 $\Gamma $ $Γ$ -invariant of tangential 2-plane fields on 3-manifolds. From our main result, we also deduce that the $\Gamma $ $Γ$ -invariant of a tangential 2-plane field on the real projective 3-space only depends on its ${{\,\textrm{d}\,}}_3$ $d_{3}$ -invariant.