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Feb 24, 2016 at 15:27 comment added Liviu Nicolaescu $\mathbb{Z}$-perfect Morse functions are automatically pseudo-regular since all the incidence numbers are $0$. Functions with only even Morse indices are perfect. Moment maps of Hamiltonian $S^1$-actions are also perfect. The map $f: U(n)\to\mathbb{R}$ $T\mapsto {\rm Re}\;(AT)$, where $A$ is a symmetric $n\times n$matrix with with simple, positive spectrum is also perfect.
Feb 24, 2016 at 15:06 comment added Mike Catanzaro Thanks for the answer. I've updated the question to clarify the situation I'm interested in.
Feb 23, 2016 at 22:17 history answered Liviu Nicolaescu CC BY-SA 3.0