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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
9
votes
Accepted
Fixed component of an $S^1$ action on $S^n$
The fixed point set need not be simply connected in general. If $M$ is any smooth homology $(n-2)$-sphere that bounds a smooth contractible $(n-1)$-manifold $W$ (such exist in abundance), then $S^1$ a …
9
votes
Accepted
Pseudofree $T^2$ actions on spheres
There is a bit of a disconnect between the title and the actual question. Usually a semifree action is one in which the only isotropy groups are the trivial group and the whole group. The actions with …
4
votes
Equivariant handle decompositions
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 …