2025/12/16 by Kegel, Marc, Nonino, Isacco, Yadav, Monika
Mathematics · Computer Science · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2512.14904
In this article, we define the contact surgery distance of two contact 3-manifolds (M,ξ) and (M',ξ') as the minimal number of contact surgeries needed to obtain (M,ξ) from (M',ξ'). Our main result states that the contact surgery distance between two contact 3-manifolds is at most 5 larger than the topological surgery distance between the underlying smooth manifolds. As a byproduct of our proof, we classify the rational homology 3-spheres on which the d3-invariant of a 2-plane field already determines its Γ-invariant and Euler class.