Regular homotopy classes of locally generic mappings
Geometric Topology
2007-05-23 v1 Algebraic Topology
Abstract
In this paper we generalize the notion of regular homotopy of immersions of a closed connected n-manifold into R^{2n-1} to locally generic mappings. The main result is that if n=2 then two mappings with singularities are regularly homotopic if and only if they have the same number of cross-cap (or Whitney-umbrella) singularities. As an application, we get a description of the path-components of the space of those immersions of a surface into R^4 whose projections into R^3 are locally generic.
Cite
@article{arxiv.math/0506563,
title = {Regular homotopy classes of locally generic mappings},
author = {Andras Juhasz},
journal= {arXiv preprint arXiv:math/0506563},
year = {2007}
}
Comments
14 pages, 5 figures