Morse index of saddle equilibria of gradient-like flows on connected sums of ${\mathbb{S}}^{n-1}\times {\mathbb{S}}^1$

Vyacheslav Grines, Elena Gurevich, Sergiy Maksymenko

Let $M$ be either $n$-sphere ${\mathbb{S}}^n$ or a connected sum of finitely many copies of ${\mathbb{S}}^{n-1}\times {\mathbb{S}}^1$, $n\ge 4$. A flow $f^t$ on $M$ is called gradien…