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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 62–64
DOI: https://doi.org/10.31857/S2686954320030170
(Mi danma73)
 

MATHEMATICS

Maps with prescribed Boardman singularities

A. D. Ryabichev

National Research University "Higher School of Economics", Moscow, Russian Federation
References:
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.
Presented: V. A. Vassiliev
Received: 12.03.2020
Revised: 12.03.2020
Accepted: 23.03.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 224–226
DOI: https://doi.org/10.1134/S1064562420030175
Bibliographic databases:
Document Type: Article
UDC: 515.16
Language: Russian
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
Citation in format AMSBIB
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\by A.~D.~Ryabichev
\paper Maps with prescribed Boardman singularities
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 492
\pages 62--64
\mathnet{http://mi.mathnet.ru/danma73}
\crossref{https://doi.org/10.31857/S2686954320030170}
\zmath{https://zbmath.org/?q=an:1477.57026}
\elib{https://elibrary.ru/item.asp?id=42930009}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 224--226
\crossref{https://doi.org/10.1134/S1064562420030175}
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