Members & Guests

Dr. Fernando Galaz García

Karlsruher Institut für Technologie

E-mail: galazgarcia(at)kit.edu
Telephone: +49 721 608 41881
Homepage: http://www.math.kit.edu/iag5/~galazg/

Publications within SPP2026

In this work, it is shown that a simply-connected, rationally-elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an almost-free, linear torus action, where this torus has rank equal to the number of odd-dimensional spherical factors in the product. As an application, simply-connected, rationally-elliptic manifolds admitting slice-maximal torus actions are classified up to equivariant rational homotopy. The case where the rational-ellipticity hypothesis is replaced by non-negative curvature is also discussed, and the Bott Conjecture in the presence of a slice-maximal torus action is proved.

 Journal Int. Math. Res. Not. IMRN Volume 18 Pages 5786--5822 Link to preprint version Link to published version

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.

Let $$M^n, n \in \{4,5,6\}$$, be a compact, simply connected n-manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible rank. Then any smooth, effective action on $$M^n$$ by a torus $$T^{n-2}$$ is equivariantly diffeomorphic to an isometric action on a normal biquotient. Furthermore, it follows that any effective, isometric circle action on a compact, simply connected, non-negatively curved four-dimensional manifold is equivariantly diffeomorphic to an effective, isometric action on a normal biquotient.