Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds

2025/06/13 by Galvin, Daniel, Nonino, Isacco · 1 citation
#57K40 (Primary) 57R52 #57N37 #57R65 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2506.11905

Abstract

We define obstructions which obstruct topological pseudo-isotopies from being isotopic to isotopies in dimension four. These match the smooth obstructions of Hatcher-Wagoner for smooth pseudo-isotopies, and accordingly are valued in certain Whitehead groups. We show that our obstructions are fully realisable, and we use these realisations to build homeomorphisms of Y× S¹ for many 3-manifolds Y that are pseudo-isotopic to the identity but not isotopic to the identity.

Cited by

• Smoothing topological pseudo-isotopies of 4-manifolds

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