An upper bound for the pseudoisotopy stable range

TL;DR

This paper establishes an upper bound for the pseudoisotopy stable range of 2n-dimensional manifolds, introduces new characteristic classes for block bundles, and discusses rational connectivity of Top(2n)/O(2n).

Contribution

It provides a new upper bound for the pseudoisotopy stable range and introduces novel characteristic classes for block bundles, extending previous work.

Findings

Pseudoisotopy stable range for 2n-manifolds is at most 2n-2.

New characteristic classes for block bundles are non-trivial.

Top(2n)/O(2n) is rationally (4n-5)-connected.

Abstract

We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than (2n-2). In order to do so, we define new characteristic classes for block bundles, extending our earlier work with Ebert, and prove their non-triviality. We also explain how similar methods show that Top(2n)/O(2n) is rationally (4n-5)-connected.