This article is cited in 1 paper

Smooth immersion of manifolds of small dimension. II. Cobordism group of critical points of multiparameter families of functions

P. M. Akhmet'ev

Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation

Abstract: The technique of studying the singularities of an I-structure developed in the first part of this paper is used to study the topological properties of the set of critical values of families of smooth functions. It turns out that certain surfaces modelling the graphics of critical values of two-parameter families of functions cannot be realized by any family (under certain additional assumptions about he separatrix manifolds). The investigation is carried out using the algebraic $K$-functor.

UDC: 515.164

MSC: 58E05, 58C27

Received: 01.03.1994

 English version: Sbornik: Mathematics, 1995, 186:12, 1727–1751

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