Non-holomorphic surface bundles and Lefschetz fibrations

TL;DR

This paper constructs infinite families of 4-manifolds as surface bundles and Lefschetz fibrations with non-zero signature that cannot admit complex structures, expanding understanding of their geometric properties.

Contribution

It demonstrates how stabilizations can produce infinitely many non-complex 4-manifolds as surface bundles and Lefschetz fibrations with non-zero signature.

Findings

Infinite families of non-complex 4-manifolds with non-zero signature

Construction of surface bundles and Lefschetz fibrations with specific genus parameters

Non-existence of complex structures for these manifolds

Abstract

We show how certain stabilizations produce infinitely many closed oriented 4-manifolds which are the total spaces of genus g surface bundles (resp. Lefschetz fibrations) over genus h surfaces and have non-zero signature, but do not admit complex structures with either orientations, for "most" (resp. all) possible values of g at least 3 and h at least 2 (resp. g at least 2 and h non-negative).