On the Hopf Problem and a Conjecture of Liu-Maxim-Wang

TL;DR

This paper explores an approach to the Hopf problem for aspherical smooth projective varieties, proposing a conjecture about the geography of aspherical surfaces of general type in complex dimension two.

Contribution

It introduces a new perspective on the Hopf problem and formulates an intriguing conjecture for aspherical surfaces of general type.

Findings

Suggests a promising approach to the Hopf problem

Proposes a conjecture on the geography of aspherical surfaces of general type

Highlights potential implications for complex dimension two

Abstract

We discuss an approach towards the Hopf problem for aspherical smooth projective varieties recently proposed by Liu, Maxim, and Wang in [LMW21]. In complex dimension two, we point out that this circle of ideas suggests an intriguing conjecture regarding the geography of aspherical surfaces of general type.