International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 721-726
doi:10.1155/S0161171288000870
The computation of the index of a Morse function at a critical point
1Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, NM, USA
2IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights 10598, NY, USA
Received 24 April 1987; Revised 12 February 1988
Copyright © 1988 Takis Sakkalis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.