Regular homotopy classes of singular maps
Geometric Topology
2007-05-23 v1 Algebraic Topology
Abstract
Two locally generic maps f,g : M^n --> R^{2n-1} are regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if n is not 3 and M^n is a closed n-manifold then the regular homotopy class of every locally generic map f : M^n --> R^{2n-1} is completely determined by the number of its singular points provided that f is singular (i.e., f is not an immersion).
Cite
@article{arxiv.math/0506566,
title = {Regular homotopy classes of singular maps},
author = {Andras Juhasz},
journal= {arXiv preprint arXiv:math/0506566},
year = {2007}
}
Comments
23 pages, 3 figures