Codimension two souls and cancellation phenomena

摘要

For each m >= 0 we find an open (4m + 9)-dimensional simply connected manifold with complete nonnegatively curved metrics whose souls are nondiffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs (N, soul) when N is the total space of a nontrivial complex line bundle over S-7 x CP2; up to diffeomorphism there are precisely three such pairs, distinguished by their nondiffeomorphic souls. (C) 2015 Elsevier Inc. All rights reserved.