A rank rigidity result for CAT(0) spaces with one-dimensional Tits boundaries
| Autor: | Russell Ricks |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Regular polygon Metric Geometry (math.MG) Group Theory (math.GR) 01 natural sciences Combinatorics Mathematics::Group Theory Rigidity (electromagnetism) Mathematics - Metric Geometry Symmetric space 0103 physical sciences Euclidean geometry FOS: Mathematics Mathematics::Metric Geometry 010307 mathematical physics 0101 mathematics Mathematics - Group Theory Mathematics |
| Zdroj: | Forum Mathematicum. 31:1317-1330 |
| ISSN: | 1435-5337 0933-7741 |
| DOI: | 10.1515/forum-2018-0133 |
| Popis: | We prove the following rank rigidity result for proper CAT(0) spaces with one-dimensional Tits boundaries: Let $\Gamma$ be a group acting properly discontinuously, cocompactly, and by isometries on such a space $X$. If the Tits diameter of $\partial X$ equals $\pi$ and $\Gamma$ does not act minimally on $\partial X$, then $\partial X$ is a spherical building or a spherical join. If $X$ is also geodesically complete, then $X$ is a Euclidean building, higher rank symmetric space, or a nontrivial product. Much of the proof, which involves finding a Tits-closed convex building-like subset of $\partial X$, does not require the Tits diameter to be $\pi$, and we give an alternate condition that guarantees rigidity when this hypothesis is removed, which is that a certain invariant of the group action be even. Comment: 14 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|