Non-trivial self-concordances and a recent conjecture by Botvinnik

TL;DR

This paper constructs non-trivial self-concordances on various manifolds, providing counterexamples to Botvinnik's recent conjecture in the field of geometric topology.

Contribution

It introduces a method to produce non-trivial concordances from the identity to itself, challenging a conjecture by Botvinnik.

Findings

Counterexamples to Botvinnik's conjecture

Existence of non-trivial self-concordances on many manifolds

Implications for geometric topology theories

Abstract

The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.