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Complements of tori in $\#_{2k}S^2 \times S^2$ that admit a hyperbolic structure (1504.06703v1)

Published 25 Apr 2015 in math.GT

Abstract: We construct examples of codimension two hyperbolic link complements in closed smooth 4-manifolds with homeomorphism type $#_{2k}S2 \times S2$. All our examples are based on a construction of J. Ratcliffe and S. Tschantz, who constructed 1171 non-compact finite volume hyperbolic 4-manifolds of minimal volume. We then give necessary conditions for a closed smooth simply connected 4-manifold to contain a codimension two link complement that admits a hyperbolic structure.

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