On Embedding Circle-Bundles in Four-Manifolds

TL;DR

This paper uses Seiberg-Witten theory to identify obstructions to splitting four-manifolds along twisted circle bundles, leading to new non-splitting results for algebraic surfaces of general type.

Contribution

It introduces novel obstructions based on Seiberg-Witten invariants that prevent certain splittings of four-manifolds along circle bundles.

Findings

Obstructions to splitting are derived from Seiberg-Witten theory.

Non-splitting results are established for algebraic surfaces of general type.

The work advances understanding of four-manifold topology and complex surface classification.

Abstract

We demonstrate an obstruction to finding certain splittings of four-manifolds along sufficiently twisted circle bundles over Riemann surfaces, arising from Seiberg-Witten theory. These obstructions are used to show a non-splitting result for algebraic surfaces of general type.