Splitting of torus representations and applications in the Grove symmetry program
Differential Geometry
2021-06-29 v1 Algebraic Topology
Abstract
A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold with positive sectional curvature has positive Euler characteristic. We prove this conjecture under the additional assumption that the isometry group has rank at least five. The fundamental new tool used to achieve this is a reduction to, and structural results concerning, a representation theoretic problem involving torus representations all of whose isotropy groups are connected.
Keywords
Cite
@article{arxiv.2106.14723,
title = {Splitting of torus representations and applications in the Grove symmetry program},
author = {Lee Kennard and Michael Wiemeler and Burkhard Wilking},
journal= {arXiv preprint arXiv:2106.14723},
year = {2021}
}