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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 3, Pages 159–202 (Mi izv8202)  

This article is cited in 2 scientific papers (total in 2 papers)

On the topology of stable Lagrangian maps with singularities of types $A$ and $D$

V. D. Sedykh

Gubkin Russian State University of Oil and Gas

Abstract: We study the topology of adjacencies of multisingularities in the image of a stable Lagrangian map with singularities of types $A_\mu^\pm$ and $D_\mu^\pm$. In particular, we prove that each connected component of the manifold of multisingularities of any fixed type $A_{\mu_1}^{\pm}\dotsb A_{\mu_p}^{\pm}$ for a germ of the image of a Lagrangian map with a monosingularity of type $D_\mu^\pm$ is either contractible or homotopy equivalent to a circle. We calculate the number of connected components of each kind for all types of multisingularities. As a corollary, we obtain new conditions for the coexistence of Lagrangian singularities.

Keywords: stable Lagrangian maps, multisingularities, adjacency index, Euler characteristic.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-5138.2014.1
This paper was written with the financial support of the President's Programme "Support of the Leading Scientific Schools of Russia" (grant no. NSh-5138.2014.1).


DOI: https://doi.org/10.4213/im8202

Full text: PDF file (827 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:3, 581–622

Bibliographic databases:

UDC: 515.16
MSC: 57R45, 53D12, 58K15
Received: 19.12.2013

Citation: V. D. Sedykh, “On the topology of stable Lagrangian maps with singularities of types $A$ and $D$”, Izv. RAN. Ser. Mat., 79:3 (2015), 159–202; Izv. Math., 79:3 (2015), 581–622

Citation in format AMSBIB
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  • https://doi.org/10.4213/im8202
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. D. Sedykh, “Topology of singularities of a stable real caustic germ of type $E_6$”, Izv. Math., 82:3 (2018), 596–611  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. D. Sedykh, “On a real caustic of type $E_6$”, Izv. Math., 85:2 (2021), 279–305  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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