Four-manifolds with shadow-complexity zero

TL;DR

This paper characterizes four-dimensional manifolds with shadow-complexity zero, showing they are composed of specific blocks and classifying those with finite fundamental groups.

Contribution

It provides a complete classification of 4-manifolds with shadow-complexity zero, linking them to 4-dimensional graph manifolds and specific decompositions.

Findings

Characterization of shadow-complexity zero 4-manifolds as graph manifolds

Classification of finite fundamental group 4-manifolds with shadow-complexity zero

Identification of particular blocks and decompositions involved

Abstract

We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces. We deduce a classification of all 4-manifolds with finite fundamental group and shadow-complexity zero.