A computable version of Hall's Harem Theorem and Geometric von Neumann Conjecture

TL;DR

This paper develops a computable version of Hall's Harem Theorem with applications to non-amenable computable coarse spaces, leading to a computable form of the geometric von Neumann conjecture.

Contribution

It introduces a computable version of Hall's Harem Theorem and applies it to establish a computable geometric von Neumann conjecture.

Findings

A computable Hall Harem Theorem with cycle size control.

Application to non-amenable computable coarse spaces.

A computable version of the geometric von Neumann conjecture.

Abstract

We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the geometric von Neumann conjecture.