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.
"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