Date/Time
Date(s) - 03/04/2025
10:00 am - 11:00 am

Speaker: Daniel Hartman (MPIM)
Research areas: Topology, Diffeomorphism groups, embeddings spaces, 4-manifolds

Location: Zoom

Title: Barbell diffeomorphism and Hatcher and Wagoner’s 2nd obstruction to pseudoisotopy implies isotopy

Abstract: Introduced by Budney and Gabai, the barbell diffeomorphisms  was used to show the existence of knotted 3-balls in the 4-sphere as well as infinitely many homotopic but not isotopic diffeomorphisms of S^1xS^3. However, barbell diffeomorphisms are not limited to the manifold S^1 x S^3. In this talk I will discuss a certain class of barbell diffeomorphism for the manifold S^1 x S^2 x I. Singh showed that the mapping class group of S^1 x S^2 x I admits an infinitely generated subgroup that are all pseudoisotopic but not isotopic to the identity. The obstruction used to distinguish these diffeomorphisms is Hatcher and Wagoner’s 2nd obstruction to the “pseudoisotopy implies isotopy” problem. The goal for the talk will be to show that the class of barbell diffeomorphisms realizes the same obstructions, and thus are pseudoisotopic but not isotopic to the identity.