Remarks on the paper "On Gromov's dihedral extremality and rigidity conjectures" by Jinmin Wang, Zhizhang Xie and Guoliang Yu

TL;DR

This paper critiques a recent work on Gromov's dihedral extremality conjecture by providing a counterexample that challenges the validity of their index computation and the resulting proof.

Contribution

It constructs a counterexample to an index calculation in the original paper, questioning the validity of their generalization of Gromov's conjecture.

Findings

Counterexample invalidates the original index computation

Challenges the proof of the generalized Gromov's dihedral extremality conjecture

Highlights the need for revised approaches in the theory

Abstract

The recent article "On Gromov's dihedral extremality and rigidity conjectures" by Jinmin Wang, Zhizhang Xie and Guoliang Yu makes a number of claims for self-adjoint extensions of Dirac type operators on manifolds with corners under local boundary conditions. We construct a counterexample to an index computation in that paper which affects the proof of its main result stating a generalisation of Gromov's dihedral extremality conjecture.