The Computation of the Index of a Morse Function at a Critical Point

A theoretical approach in computing the index of a Morse function at a critical point on a real non-singular hypersurface V is given. As a consequence the Euler characteristic of V is computed. In the case where the hypersurface is polynomial and compact, a procedure is given that finds a linear function l, whose restriction l∣v, is a Morse function on V. © 1988, Hindawi Publishing Corporation. All rights reserved.