Proof of Kitaev determinant trivialization conjecture

TL;DR

This paper proves a conjecture in algebraic K-theory related to the trivialization of the Fredholm determinant of a multiplicative commutator using Kitaev's criterion.

Contribution

It establishes a proof of the Kitaev determinant trivialization conjecture leveraging algebraic K-theory techniques.

Findings

Proof of the Kitaev determinant trivialization conjecture.

Application of algebraic K-theory to operator theory.

Simplification of criteria for trivializing Fredholm determinants.

Abstract

Using ideas from algebraic $K$-theory, we prove that a simple and naturally applicable criterion of Kitaev suffices to trivialize the Fredholm determinant of a multiplicative commutator.