2009/12/24 by Belegradek, Igor, Kwasik, Slawomir, Schultz, Reinhard
#53C20 #57R55 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0912.4874
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.