Eliashberg's $h$-principle and generic maps of surfaces with prescribed singular locus
Geometric Topology
2023-11-30 v3
Abstract
We extend Y.Eliashberg's -principle to smooth maps of surfaces which are allowed to have cusp singularities, as well as folds. More precisely, we prove a necessary and sufficient condition for a given map of surfaces to be homotopic to one with given loci of folds and cusps. Then we use these results to obtain a necessary and sufficient condition for a subset of a surface to be realizable as the critical set of some generic smooth map from to a given surface .
Keywords
Cite
@article{arxiv.1810.00205,
title = {Eliashberg's $h$-principle and generic maps of surfaces with prescribed singular locus},
author = {Andrey Ryabichev},
journal= {arXiv preprint arXiv:1810.00205},
year = {2023}
}
Comments
18 pages, 10 figures; the article was eleborated