Torus actions on rationally elliptic manifolds

TL;DR

This paper establishes an upper limit on the size of torus groups acting smoothly on certain rationally elliptic manifolds and classifies those with maximal rank actions.

Contribution

It provides a new upper bound for torus action ranks and classifies manifolds with maximal torus actions up to equivariant rational homotopy type.

Findings

Upper bound on torus action rank

Classification of manifolds with maximal torus actions

Effective torus actions on rationally elliptic manifolds

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.