Actions on positively curved manifolds and boundary in the orbit space
Abstract
We study isometric actions of compact Lie groups on complete orientable positively curved -manifolds whose orbit spaces have non-empty boundary in the sense of Alexandrov geometry. In particular, we classify quotients of the unit sphere by actions of compact simple Lie groups with non-empty boundary. We deduce from this the list of representations of compact simple Lie groups that admit non-trivial reductions. As a tool of special interest, we introduce a new geometric invariant of a compact symmetric space, namely, the minimal number of points in a "spanning set" of the space.
Keywords
Cite
@article{arxiv.2112.00513,
title = {Actions on positively curved manifolds and boundary in the orbit space},
author = {Claudio Gorodski and Andreas Kollross and Burkhard Wilking},
journal= {arXiv preprint arXiv:2112.00513},
year = {2024}
}
Comments
Added explanations to proof of Theorem 1.6 and filled gap in proof of Corollary 1.5. Added proof of Theorem 1.1. Rewrote proof of Lemma 3.1. Corrected statement and proof of Corollary 7.3. Other minor changes