Second obstruction to pseudoisotopy in dimension 3

2021/12/15 by Igusa, Kiyoshi
#19J10: 58K60 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2112.08293

Abstract

We use lens-shaped models and the second obstruction to pseudoisotopy to construct a nontrivial diffeomorphism of M× I where M is the connected sum of S¹× S² with a another nonsimply connected 3-manifold M'. Then we take two copies of this diffeomorphism and paste together their tops and bottoms to obtain a diffeomorphism of M× S¹. Properties of the second obstruction and the first Postnikov invariant imply that this diffeomorphism of the closed 4-manifold M× S¹ is not isotopic to the identity. Similar results were obtain by Singh [10].

Related

• Second obstruction to pseudoisotopy I
• Pseudo-isotopies and diffeomorphisms of 4-manifolds
• Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds
• A note on homotopy and pseudoisotopy of diffeomorphisms of 4-manifolds
• Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres