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2020 Shadows of acyclic $4$–manifolds with sphere boundary
Yuya Koda, Hironobu Naoe
Algebr. Geom. Topol. 20(7): 3707-3731 (2020). DOI: 10.2140/agt.2020.20.3707

Abstract

In terms of Turaev’s shadows, we provide a sufficient condition for a compact, smooth, acyclic 4–manifold with boundary the 3–sphere to be diffeomorphic to the standard 4–ball. As a consequence, we prove that if a compact, smooth, acyclic 4–manifold with boundary the 3–sphere has shadow-complexity at most 2, then it is diffeomorphic to the standard 4–ball.

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Yuya Koda. Hironobu Naoe. "Shadows of acyclic $4$–manifolds with sphere boundary." Algebr. Geom. Topol. 20 (7) 3707 - 3731, 2020. https://doi.org/10.2140/agt.2020.20.3707

Information

Received: 11 October 2019; Revised: 9 March 2020; Accepted: 26 March 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194291
Digital Object Identifier: 10.2140/agt.2020.20.3707

Subjects:
Primary: 57N13
Secondary: 57M20 , 57R55 , 57R65

Keywords: $4$–manifold , differentiable structure , handlebody , polyhedron , Shadow

Rights: Copyright © 2020 Mathematical Sciences Publishers

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