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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2015 Volume 79, Issue 3, Pages 159–202 (Mi im8202)

This article is cited in 6 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.

UDC: 515.16

MSC: 57R45, 53D12, 58K15

Received: 19.12.2013

DOI: 10.4213/im8202


 English version:
Izvestiya: Mathematics, 2015, 79:3, 581–622

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