Second obstruction to pseudoisotopy I

TL;DR

This paper constructs specific pseudoisotopies of 4-manifolds to realize elements of the second obstruction to pseudoisotopy, advancing understanding of diffeomorphism classes in 4-dimensional topology.

Contribution

It provides an explicit construction of pseudoisotopies in 4-manifolds related to the second obstruction, with future work extending to 5-manifolds.

Findings

Explicit pseudoisotopy constructions for 4-manifolds

Realization of second obstruction elements

Foundation for further 5-manifold results

Abstract

A pseudoisotopy of $M$ is a diffeomorphism of $M\times I$ which is the identity on $M\times 0$. We give an explicit construction of pseudoisotopies of 4-manifolds which realize certain elements of the "second obstruction to pseudoisotopy". The next paper will give precise statements of our results for 5-manifolds which had been announced long ago.