Donaldson invariants for some glued manifolds

TL;DR

This paper proves that certain 4-manifolds with specific topological features are of simple type and establishes a relationship between their Donaldson invariants and those of connected sums along a genus 2 Riemann surface.

Contribution

It introduces new results on the simple type property of 4-manifolds with genus 2 embedded surfaces and relates their invariants through connected sums.

Findings

Proves 4-manifolds with $b_1=0$ and genus 2 surfaces are of simple type.

Establishes a relationship between basic classes of these manifolds and their connected sums.

Advances understanding of Donaldson invariants in complex 4-manifold constructions.

Abstract

We prove that every suitable $4$-manifold with $b_1=0$ and with an embedded Riemann surface of genus $2$ is of simple type. We find a relationship between the basic classes of two of these $4$-manifolds and those of the connected sum along the Riemann surface.