Corks with large shadow-complexity and exotic 4-manifolds

Abstract

We construct an infinite family $\{C_{n,k}{\}}_{k=1}^{\infty }$ of corks of Mazur type satisfying $2n\le {\mathrm{sc}}^{\mathrm{sp}}(C_{n,k})\le O(n^{3/2})$ for any positive integer $n$. Furthermore, using these corks, we construct an infinite family $\{(W_{n,k},W_{n,k}^{\prime }){\}}_{k=1}^{\infty }$ of exotic pairs of $4$-manifolds with boundary whose special shadow-complexities satisfy the above inequalities. We also discuss exotic pairs with small shadow-complexity.

27 pages, 20 figures

References in corpus (3)

• Corks, Plugs and exotic structures
• Mazur manifolds and corks with small shadow complexities
• Boundary-sum irreducible finite order corks