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Shadows of acyclic
$4$–manifolds with sphere boundary
Yuya Koda and Hironobu Naoe |
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Algebraic & Geometric Topology 20 (2020) 3707–3731
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Abstract |
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In terms of Turaev’s shadows, we provide a sufficient condition for a compact, smooth, acyclic –manifold with boundary the –sphere to be diffeomorphic to the standard –ball. As a consequence, we prove that if a compact, smooth, acyclic –manifold with boundary the –sphere has shadow-complexity at most , then it is diffeomorphic to the standard –ball. |
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Keywords
$4$–manifold, shadow, differentiable structure, handlebody,
polyhedron
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Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 57M20, 57R55, 57R65
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References |
Publication
Received: 11 October 2019
Revised: 9 March 2020
Accepted: 26 March 2020
Published: 29 December 2020
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Authors |
| Yuya Koda | |
| Department of Mathematics Hiroshima University Hiroshima Japan |
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| Hironobu Naoe | |
| Department of Mathematics Chuo University Tokyo Japan |
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