Volume 20, issue 7 (2020)

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Shadows of acyclic $4$–manifolds with sphere boundary

Yuya Koda and Hironobu Naoe

Algebraic & Geometric Topology 20 (2020) 3707–3731

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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$4$–manifold, shadow, differentiable structure, handlebody, polyhedron
Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 57M20, 57R55, 57R65
Received: 11 October 2019
Revised: 9 March 2020
Accepted: 26 March 2020
Published: 29 December 2020
Yuya Koda
Department of Mathematics
Hiroshima University
Hironobu Naoe
Department of Mathematics
Chuo University