余维双灵魂与消去现象
Codimension two souls and cancellation phenomena
摘要：
对于每一个非负整数，我们发现一个开放的（4 m +9）维单连通流形承认完整的非负弯曲的度量，其灵魂是非同构，同胚，并有余维2。当N是7-球面和复射影平面的乘积上的非平凡复线丛时，我们给出了对（N，soul）的一个复同态分类：直到复同态，正好有三个这样的对，以它们的非复同态的soul来区分.
英文摘要：
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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