Mo | Di | Mi | Do | Fr | Sa | So |
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 |
8 | 9 | 10 | 11 | 12 | 13 | 14 |
15 | 16 | 17 | 18 | 19 | 20 | 21 |
22 | 23 | 24 | 25 |
26 | 27 | 28 |
29 | 30 | 1 | 2 | 3 | 4 | 5 |
In the last decade CAT(0) cube complexes have gotten a lot of attention in geometric group theory and related areas. This comes from the fact that many groups are “cubulated”, i.e. act proper cocompactly on a CAT(0) cube complex (e.g. RAAGs, RACGs, hyperbolic 3-manifold groups), and that such an action (called “cubulation”) allows to derive interesting algebraic properties of the group; a prominent example of that is the “recent” proof of the virtual Haken conjecture. We want to point out that in general a group admits many non-isomorphic cubulations; which is why we want to consider the following rigidity question of cubulations (called “marked length spectrum rigidity”): Let G be a group that acts cocompactly on two irreducible CAT(0) cube complexes X,Y. Assume that the translation lengths for all g in G are the same for the action on X and on Y. Are X and Y then G-equivariantly isomorphic? In this talk we show that with the right choice of metric and under some natural assumptions (e.g. no free faces) this holds if adding a small assumption on X or Y. If X and Y show low-dimensional behaviour (e.g. square-complexes or particular cubulations of surface groups), then the statement is true in full generality. To proof this, we construct a notion of cross ratio on particular boundaries of the cube complexes - generalising a classical object on boundaries of negatively curved spaces - and show that the boundary equipped with the cross ratio determines the isomorphism type of the cube complex. This is joint work with E. Fioravanti and M. Incerti-Medici.
Dienstag, den 6. November 2018 um 13:00 Uhr, in INF205, SRC Dienstag, den 6. November 2018 at 13:00, in INF205, SRC
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Anna Wienhard, Prof. Dr. Peter Albers