Codimension two souls and cancellation phenomena

Details Codimension two souls and cancellation phenomena Codimension two souls and cancellation phenomena

2009-12-24

arxiv.org/abs/0912.4874v1

Mathematics

Differential Geometry

34 pages

Scientific paper

For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs (N, soul) when N is a nontrivial complex line bundle over the product of 7-sphere and complex projective plane: up to diffeomorphism there are precisely three such pairs, distinguished by their non-diffeomorphic souls.

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