Geodesic
Semi-Free Actions with Manifold Orbit Spaces
Documenta mathematica, Tome 25 (2020), pp. 2085-2114.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply connected $5$-manifolds admitting a smooth, semi-free circle action with fixed-point components of codimension $4$ are connected sums of $\mathbf{S}^3$-bundles over $\mathbf{S}^2$. Furthermore, the Betti numbers of the $5$-manifolds and of the quotient $4$-manifolds are related by a simple formula involving the number of fixed-point components. We also investigate semi-free $S^3$ actions on simply connected $8$-manifolds with quotient a $5$-manifold and show, in particular, that there are strong restrictions on the topology of the $8$-manifold.
Classification : 57S17, 55R55, 57K50
Keywords: circle action, semi-free action, \(5\)-manifolds, \(4\)-manifolds, \(8\)-manifolds 
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     author = {Harvey, John and Kerin, Martin and Shankar, Krishnan},
     title = {Semi-Free {Actions} with {Manifold} {Orbit} {Spaces}},
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Harvey, John; Kerin, Martin; Shankar, Krishnan. Semi-Free Actions with Manifold Orbit Spaces. Documenta mathematica, Tome 25 (2020), pp. 2085-2114. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a13/