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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Unstable bordism groups and isolated singularities


Author: David Ellis
Journal: Trans. Amer. Math. Soc. 274 (1982), 695-708
MSC: Primary 57R75
MathSciNet review: 675075
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Abstract: An isolated singularity of an embedded submanifold can be topologically smoothed if and only if a certain obstruction element in $ {\pi _ \ast }(MG)$ vanishes, where $ G$ is the group of the normal bundle. In fact this obstruction lies in a certain subgroup which is referred to here as the unstable $ G$-bordism group. In this paper some of the unstable $ SO$-bordism groups are computed; the obstruction to smoothing the complex cone on an oriented submanifold $ X \subset \mathbf{C}{P^n}$ at $ \infty$ is computed in terms of the characteristic numbers of $ X$. Examples of nonsmoothable complex cone singularities are given using these computations.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0675075-9
PII: S 0002-9947(1982)0675075-9
Article copyright: © Copyright 1982 American Mathematical Society