Corks with Large Shadow-Complexity and Exotic Four-Manifolds

We construct an infinite family {C-n,C-k}(k=1)(infinity) of corks of Mazur type satisfying 2n <= sc(sp)(C-n,C-k) <= O(n(3/2)) for any positive integer n. Using these corks, we construct an infinite family {(W-n,W-k, W-n,W-k' )}(k=1)(infinity) 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.