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09 February 2025
 
  » arxiv » 1605.0250

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Shadows of 4-manifolds with complexity zero and polyhedral collapsing
Hironobu Naoe ;
Date 1 May 2016
AbstractOur purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on structures of almost-special polyhedra and discuss this problem combinatorially. We prove that any polyhedral collapsing does not change 4-manifolds obtained by Turaev’s reconstruction from almost-special polyhedra before and after collapsing. We also show that any acyclic simple polyhedron without true vertices can collapse onto a disk. As a consequence of these results, we prove that any acyclic 4-manifold having shadow complexity zero with boundary is diffeomorphic to a 4-ball.
Source arXiv, 1605.0250
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