L^2-Betti numbers in prime characteristic and a conjecture of Wise

TL;DR

This paper investigates L^2-Betti numbers in different characteristics and explores their relation to Wise's conjecture about towers of finite 2-complexes and the second L^2-Betti number.

Contribution

It provides a systematic study of L^2-Betti numbers in various characteristics and applies findings to analyze Wise's conjecture.

Findings

L^2-Betti numbers are systematically studied in zero and prime characteristic.

The paper relates the vanishing of the second L^2-Betti number to Wise's conjecture.

Results suggest a connection between L^2-Betti numbers and properties of towers of 2-complexes.

Abstract

We systematically study L^2-Betti numbers in zero and prime characteristic and apply them to a conjecture of Wise stating that all towers of a finite 2-complex are non-positive if and only if the second L^2-Betti number vanishes.