Morse–Bott inequalities in the presence of a compact Lie group action and applications

In this paper, we obtain Morse–Bott inequalities in the presence of a compact Lie group action via Bismut–Lebeauʼs analytic localization techniques. As an application, we obtain Morse–Bott inequalities on compact manifold with nonempty boundary by applying the generalized Morse–Bott inequalities to the doubling manifold.