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arXiv · 0807.4894

Complex cobordisms and singular manifolds arising from Chern classes

Andrei Kustarev
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Abstract

This paper deals with the question of J.Morava on existence of canonical complex cobordism class of singular submanifold. We present several solutions of this question for $X_r(ξ)$ -- the set of points where $\dimξ-r+1$ generic sections of a complex vector bundle $ξ$ are linearly dependent. The corresponding complex cobordism classes $Q_r(ξ)$ and $P_r(ξ)$ tend to have many nice properties, such as deformed sum formula, but they don't coincide with Chern classes $c_r^U(ξ)$. They also have relation to the theory of $IH$-small resolutions.

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Andrei Kustarev. 2008-07-30. Complex cobordisms and singular manifolds arising from Chern classes. https://arxiv.org/abs/0807.4894

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