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THE EULER CHARACTERISTIC OF THE FIBER PRODUCT OF MORSE FUNCTIONS ON THE UNITARY GROUP
Keywords:
fiber product, Morse function, unitary groupDOI:
https://doi.org/10.17654/0972415X25004Abstract
It is well known that corresponding to a choice of real numbers $0<c_1<c_2<\cdots<c_n$, we obtain the canonical Morse function $f$ on $U(n)$. We denote by $C(f)$ the fiber product of two copies of $f$. We fix a positive integer $p$ and set $c_i=i^p$ for $1 \leq i \leq n$. In this case, we denote the Morse function by $f_{n, p}$. We determine $\chi\left(C\left(f_{n, p}\right)\right)$. Our result generalizes the previous result for the case $p=1$.
Received: May 5, 2025
Accepted: June 11, 2025
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