Regular homotopy classes of locally generic mappings

Details Regular homotopy classes of locally generic mappings Regular homotopy classes of locally generic mappings

2005-06-28

arxiv.org/abs/math/0506563v1

Topology Appl. 138 (2004), no. 1-3, 45--59

Mathematics

Geometric Topology

14 pages, 5 figures

Scientific paper

10.1016/j.topol.2003.07.004

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.

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