Complex cobordisms and singular manifolds arising from Chern classes

2008/07/30 by Andrei Kustarev, Kustarev, Andrei
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT

paper · pdf · doi:10.48550/arxiv.0807.4894

arxiv created 2008/07/30 · arxiv updated 2009/12/01

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.

Related

• Cobordism Obstructions to Complex Sections
• Cobordism of singular maps
• Complex cobordism classes of homogeneous spaces
• The smooth center of the cohomology of a singular variety
• Enumeration of singular varieties with tangency conditions