TY - JOUR
T1 - Shadows of acyclic 4-manifolds with sphere boundary
AU - Koda, Yuya
AU - Naoe, Hironobu
N1 - Funding Information:
The authors wish to express their gratitude to Kouichi Yasui for many helpful comments. They would like to thank the anonymous referee for his or her valuable comments and suggestions which helped them to improve the exposition. Koda is supported in part by JSPS KAKENHI Grant Numbers 15H03620, 17K05254, 17H06463, and JST CREST Grant Number JPMJCR17J4. Naoe is supported by JSPS KAKENHI Grant Number 18H05827.
Publisher Copyright:
© 2020, Mathematical Science Publishers. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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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U2 - 10.2140/agt.2020.20.3707
DO - 10.2140/agt.2020.20.3707
M3 - Article
AN - SCOPUS:85100751913
SN - 1472-2747
VL - 20
SP - 3707
EP - 3731
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 7
ER -