Obstructions to the existence of fold maps

Details Obstructions to the existence of fold maps Obstructions to the existence of fold maps

2010-03-14

arxiv.org/abs/1003.2754v1

J. London Math. Soc. (2) 81 (2010) 338-354

Mathematics

Algebraic Topology

17 pages; the final version of the preprint will be published in the Journal of the LMS

Scientific paper

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in terms of characteristic classes, which arise as Postnikov invariants, and can be interpreted as primary and secondary obstructions to the elimination of certain singularities. We also discuss the relationship between the existence problem of fold maps and that of vector fields of stabilized tangent bundles.

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