Shadows of acyclic 4–manifolds with sphere boundary

Koda, Yuya; Naoe, Hironobu

doi:10.2140/agt.2020.20.3707

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Shadows of acyclic $4$–manifolds with sphere boundary

Yuya Koda and Hironobu Naoe

Algebraic & Geometric Topology 20 (2020) 3707–3731

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.

Keywords

$4$–manifold, shadow, differentiable structure, handlebody, polyhedron

Mathematical Subject Classification 2010

Primary: 57N13

Secondary: 57M20, 57R55, 57R65

References

Publication

Received: 11 October 2019

Revised: 9 March 2020

Accepted: 26 March 2020

Published: 29 December 2020

Authors

Yuya Koda
Department of Mathematics Hiroshima University Hiroshima Japan

Hironobu Naoe
Department of Mathematics Chuo University Tokyo Japan

Volume 20, issue 7 (2020)