Shadows of 4-manifolds with complexity zero and polyhedral collapsing

Hironobu Naoe

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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 X0 that is obtained by collapsing from X. Then we prove that there exists a canonical way to equip internal regions of X0 with gleams so that two 4-manifolds reconstructed from X0 and X are diffeomorphic. We also show that any acyclic simple polyhedron whose singular set is a union of circles 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.

本文言語English
ページ(範囲)4561-4572
ページ数12
ジャーナルProceedings of the American Mathematical Society
145
10
DOI
出版ステータスPublished - 2017
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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