A Formula for the Euler Characteristic of the Fiber Product of Morse Functions
Abstract
Let η:X→R be a Morse function on a connected closed manifold X. We denote by C(η) the fiber product of two copies of η. For Morse functions f:M→R and g:N→R, we define the function f∗g:M×N→R by (f∗g)(p,q):=f(p)·g(q). The purpose of this paper is twofold: Firstly, we study the sufficient condition for which χ(C(f∗g))=χ(C(f))·χ(C(g)) holds, where χ denotes the Euler characteristic. Secondly, for the case that f is the well-known Morse function on CPn, we determine χ(C(f∗f)).
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometry and complex manifolds
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- International Journal of Topology
- Publisher
- MDPI AG
- Volume
- 3
- Issue
- 1
- Pages
- 4–4
- Publication date
- 9 February 2026
- Language
- EN