The Morse–Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse–Bott function defined on it. The Morse–Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample and clarify the origin of the mistake.
|Number of pages||2|
|Journal||Comptes rendus de l'Académie des Sciences. Série I, Mathématique|
|Publication status||Published - 1 Oct 2016|