# Complex cobordisms and singular manifolds arising from Chern classes

Authors
Type
Preprint
Publication Date
Jul 30, 2008
Submission Date
Jul 30, 2008
Source
arXiv
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 $X_r(\xi)$ -- the set of points where $\dim\xi-r+1$ generic sections of a complex vector bundle $\xi$ are linearly dependent. The corresponding complex cobordism classes $Q_r(\xi)$ and $P_r(\xi)$ tend to have many nice properties, such as deformed sum formula, but they don't coincide with Chern classes $c_r^U(\xi)$. They also have relation to the theory of $IH$-small resolutions.