# A.A. Agrachev, R.V. Gamkrelidze, Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets

Title: Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets
Authors: A.A. Agrachev, R.V. Gamkrelidze
Journal title: Journal of Soviet Mathematics
Year: 1991
Volume: 55
Pages: 1892–1928
Citation:

A. A. Agrachev, R. V. Gamkrelidze, “Quadratic mappings and smooth vector functions: Euler characteristics of level sets”, Journal of Soviet Mathematics, 1991, 55:4, 1892–1928

Abstract:

Quadratic maps of $R^N$ into $R^K$ are studied. Explicit expressions are obtained for the Euler characteristics of level sets of such maps. The Euler characteristics of level sets of smooth vector-valued functions are also evaluated in terms of their values at critical points.