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John Pardon
John Pardon
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This foundational paper: Arthur G. Wasserman, Equivariant Differential Topology, Topology, 8(1967), 127-150, has section 4 dealing with equivariant Morse theory for manifolds with a smooth action of a compact Lie group, including equivariant handle attaching, equivariant Morse Lemma, etc. See MathSciNet ReviewMathSciNet Review. The last result of the paper concludes that a compact G-manifold is a union of "handle bundles over orbits".

This foundational paper: Arthur G. Wasserman, Equivariant Differential Topology, Topology, 8(1967), 127-150, has section 4 dealing with equivariant Morse theory for manifolds with a smooth action of a compact Lie group, including equivariant handle attaching, equivariant Morse Lemma, etc. See MathSciNet Review. The last result of the paper concludes that a compact G-manifold is a union of "handle bundles over orbits".

This foundational paper: Arthur G. Wasserman, Equivariant Differential Topology, Topology, 8(1967), 127-150, has section 4 dealing with equivariant Morse theory for manifolds with a smooth action of a compact Lie group, including equivariant handle attaching, equivariant Morse Lemma, etc. See MathSciNet Review. The last result of the paper concludes that a compact G-manifold is a union of "handle bundles over orbits".

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Allan Edmonds
Allan Edmonds
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This foundational paper: Arthur G. Wasserman, Equivariant Differential Topology, Topology, 8(1967), 127-150, has section 4 dealing with equivariant Morse theory for manifolds with a smooth action of a compact Lie group, including equivariant handle attaching, equivariant Morse Lemma, etc. See MathSciNet Review. The last result of the paper concludes that a compact G-manifold is a union of "handle bundles over orbits".