Classifying $VII_0$ surfaces with $b_2 = 0$ via group theory

TL;DR

This paper provides a new group-theoretic proof of a classification theorem for certain complex surfaces, specifically $VII_0$ surfaces with $b_2=0$, confirming they are Hopf or Inoue surfaces.

Contribution

It introduces a purely group-theoretic approach to classify $VII_0$ surfaces with $b_2=0$, offering an alternative proof to Bogomolov's theorem.

Findings

Confirmed that $VII_0$ surfaces with $b_2=0$ are Hopf or Inoue surfaces

Provided a new proof strategy based solely on group theory

Simplified understanding of the classification of these surfaces

Abstract

We give a new proof of a theorem of Bogomolov, that the only $VII_0$ surfaces with $b_2 = 0$ are those constructed by Hopf and Inoue. The proof follows the strategy of the original one, but it is of purely group-theoretic nature.