Self-coincidences in higher codimensions

Ulrich Koschorke

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arXiv · math/0606033

Self-coincidences in higher codimensions

Ulrich Koschorke

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Abstract

When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers our question completely in a large dimension range. As an illustration we give explicit criteria in three sample settings: projections from Stiefel manifolds to Grassmannians, sphere bundle projections and maps defined on spheres. In the first example a theorem of Becker and Schultz concerning the framed bordism class of a compact Lie group plays a central role; our approach yields also a very short geometric proof (included as an appendix) of this result.

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BibTeX RIS

Ulrich Koschorke. 2006-06-01. Self-coincidences in higher codimensions. https://arxiv.org/abs/math/0606033

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