Knot concordances in S1×S^2 and exotic smooth 4-manifolds
It is known that there is a unique concordance class in the free homotopy class of S1 × pt ⊂ S1 × S2. The constructive proof of this fact is given by the second author. It turns out that all the concordances in this construction are invertible. The knots K ⊂ S1 × S2 with hyperbolic complements and trivial symmetry group are special interest here, because they can be used to gener- ate absolutely exotic compact 4-manifolds by the recipe given by Akbulut and Ruberman. Here we built absolutely exotic manifold pairs by this construction, and show that this construction keeps the Stein property of the 4-manifolds we start out with. By using this we establish the existence of an absolutely exotic contractible Stein manifold pair, and absolutely exotic homotopy S1 ×B3 Stein manifold pair.
