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Results tagged with alexandrov-geometry
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user 7021
Alexandrov geometry studies non smooth analogues of Riemannian manifolds with curvature bounded from below or above. It includes spaces with curvature bounded below (briefly $\mathrm{CBB}[\kappa]$) and spaces with curvature bounded above (briefly $\mathrm{CAT}[\kappa]$).
2
votes
Accepted
Flat sector in a proper cocompact CAT(0) space
Xie proved that this is true if $X$ is a 2 dimensional complex. I recommend reading his article: "The Tits Boundary of a CAT(0) 2-Complex", Trans. AMS., 357, no. 4, 1627-1661. I think that the answ …
- 1,371
8
votes
Accepted
Contracting a geodesic on a space of curvature less than 1
There is an article by B. Bowditch, Notes on locally CAT(1) spaces, in Geometric Group Theory, R.Charney, M.Davis, and M.Shapiro eds., de Gruyter (1995) that will likely be of help. The article is a …
- 1,371
12
votes
Braid groups acting on CAT(0)-complexes
This is an open problem. The answer is yes for $B_3$: it acts geometrically on a regular degree three tree crossed with the real line. I learned of this construction in an article by Tom Brady and Jo …
- 1,371