Deformation equivalence classes of complex surfaces with the first Betti number one, and the second Betti number zero

TL;DR

This paper proves that there are finitely many deformation equivalence classes of complex surfaces with specific Betti numbers, providing a classification result in complex surface theory.

Contribution

It establishes the finiteness of deformation classes for complex surfaces with first Betti number one and second Betti number zero, under homotopy equivalence.

Findings

Finiteness of deformation equivalence classes proven

Applicable to surfaces homotopy equivalent to certain 4-manifolds

Advances classification of complex surfaces with given Betti numbers

Abstract

We will prove that the number of deformation equivalence classes of surfaces homotopy equivalent to a smooth, closed 4-manifold is finite, if the first Betti number is equal to one, and the second Betti number is equal to zero.