Torus actions on rationally elliptic manifolds

2015/11/26 by Galaz-Garcia, Fernando, Kerin, Martin, Radeschi, Marco
#55P62 #57R91 #57S15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1511.08383

Abstract

An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed, simply connected, rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up to equivariant rational homotopy type.

Related

• The Toral Rank Conjecture and variants of equivariant formality
• Rational toral rank of a map
• ℤ_p-torus actions on positively curved manifolds
• On the Rational Hyperbolicity problem
• Torus Actions, Fixed-Point Formulas, Elliptic Genera and positive curvature