# Codimension two souls and cancellation phenomena

## TL;DR

This paper constructs high-dimensional, simply-connected manifolds with nonnegative curvature that contain pairs of non-diffeomorphic, homeomorphic souls of codimension 2, and classifies certain diffeomorphism types involving complex line bundles.

## Contribution

It demonstrates the existence of manifolds with nonnegative curvature having non-diffeomorphic souls of codimension 2 and classifies specific pairs involving complex line bundles over 7-sphere and complex projective plane.

## Key findings

- Existence of manifolds with non-diffeomorphic, homeomorphic souls of codimension 2.
- Classification of pairs (N, soul) over certain complex line bundles.
- Identification of exactly three such diffeomorphism classes.

## Abstract

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.