# Shadows of 4-manifolds with complexity zero and polyhedral collapsing

@article{Naoe2016ShadowsO4, title={Shadows of 4-manifolds with complexity zero and polyhedral collapsing}, author={Hironobu Naoe}, journal={arXiv: Geometric Topology}, year={2016} }

Our purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on simple polyhedra and discuss this problem combinatorially. We consider a shadowed polyhedron $X$ and a simple polyhedron $X_0$ that is obtained by collapsing from $X$. Then we prove that there exists a canonical way to equip internal regions of $X_0$ with gleams so that two 4-manifolds reconstructed from $X_0$ and $X$ are diffeomorphic. We also show that any acyclic simple polyhedron whose…

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