The formula describes the euler characteristic of the fiber product of two Morse functions, providing key insights into their properties.
Specifically, it characterizes χ(C(f)), revealing the underlying structure of fiber products generated by Morse functions.
This analysis employs advanced mathematical concepts such as grassmannians and fiber products, essential in topology studies.
Understanding these relationships helps to deepen knowledge in topology, particularly regarding Morse theory and grassmannians.
Abstract
For , , or , let denote the Grassmannian of k ‐planes in . For a well‐known Morse function , we denote by C ( f ) the fiber product of two copies of f . We prove a formula which describes χ ( C ( f )).