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Let $G$ be a Lie group acting properly on a smooth manifold $M$. The (non-equivariant) definition of a Morse function does not carry over to equivariant functions $M \rightarrow \mathbb{R}$ (where $\...

This question was posed on Math.SE but no one has answered it; it may be suitable for MathOverflow. Let $D$ be the Dirac operator on $\mathbb{R}^n$ i.e. $D=\sum_{j=1}^nE_j\frac{\partial}{\partial ...

Can anyone give me a reference which precisely stated the definition of an equivariant connection and equivariant curvature? Precisely, If G be a compact lie group acting linearly on a smooth ...

Let $G$ be a compact Lie group which act on a manifold $M$. We fix this action throughout our question. Assume that $E\to M$ is a vector bundle which has the potential of admitting ...