Morse-Bott inequalities in the presence of a compact Lie group action and applications (Q389351)

Let \(M\) be a smooth \(n\)-dimensional closed and connected manifold, and let \(G\) be a compact Lie group acting smoothly on \(M\). In this very interesting paper, the author obtains Morse-Bott inequalities under the action of \(G\). More precisely, he gets Morse inequalities for the multiplicities of the irreducible representations of \(G.\) Furthermore, by passing to the doubling manifold, Morse-Bott inequalities for manifolds with nonempty boundary are also obtained.