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The Euler characteristic of the fiber product of Morse functions
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For a Morse function $f: M \to \R$ on a connected closed manifold $M$, we denote by $C(f)$ the fiber product of two copies of $f$. We prove a formula which describes $\chi (C(f))$. As an application, we consider two Morse functions on $U(n)$. We obtain the result that $\chi (C(f))$ is $(-2)^n$ or a certain number which originated in dynamics.
Abstract
For a Morse function $f: M \to \R$ on a connected closed manifold $M$, we denote by $C(f)$ the fiber product of two copies of $f$. We prove a formula which describes $\chi (C(f))$. As an application, we consider two Morse functions on $U(n)$. We obtain the result that $\chi (C(f))$ is $(-2)^n$ or a certain number which originated in dynamics.
관련 논문AI추천
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