Conjugation spaces and 4-manifolds

TL;DR

This paper demonstrates that all 4-dimensional conjugation manifolds can be constructed via branched 2-fold coverings over knotted surfaces within Z/2-homology 4-spheres, providing a unifying perspective on their topology.

Contribution

It establishes a comprehensive construction method for 4-dimensional conjugation manifolds using branched coverings over knotted surfaces.

Findings

All 4-dimensional conjugation manifolds are obtained from branched 2-fold coverings.

The construction involves knotted surfaces in Z/2-homology 4-spheres.

Provides a classification framework for these manifolds.

Abstract

We show that 4-dimensional conjugation manifolds are all obtained from branched 2-fold coverings of knotted surfaces in Z/2-homology 4-spheres.