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MATHEMATICS
Maps with prescribed Boardman singularities
A. D. Ryabichev National Research University "Higher School of Economics", Moscow, Russian Federation
Abstract:
In this paper we extend Y. Eliashberg's theorem on the maps with fold type singularities to arbitrary Thom-Boardman singularities. Namely, we state a necessary and sufficient condition for a continuous map of smooth manifolds of the same dimension to be homotopic to a generic map with a prescribed Thom-Boardman singularity $\Sigma^I$ at each point. In dimensions 2 and 3 we rephrase this condition in terms of the homology classes of the given singular loci and the characteristic classes of the manifolds.
Keywords:
Thom-Boardman singularities, folds, cusps, $h$-principle.
Citation:
A. D. Ryabichev, “Maps with prescribed Boardman singularities”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 62–64; Dokl. Math., 101:3 (2020), 224–226
Linking options:
https://www.mathnet.ru/eng/danma73 https://www.mathnet.ru/eng/danma/v492/p62
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