Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres

2025/05/17 by Gabai, David, Gay, David T., Hartman, Daniel · 1 citation
#57N37 (Secondary) #57R35 (Primary) 57R52 #57R50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2505.12088

Abstract

We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in S² × S² and in connected sums of S² × S². that cannot be homotoped to a loops of spheres dual to the standard horizontal sphere. In the sequel [GGH], we will use these techniques to expand upon the applicability of the invariant and prove Diff⁺(S⁴) has an exotic element.

Cited by

• On absolutely exotic diffeomorphisms of 4-manifolds

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