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- W2146165986 abstract "We describe a connection between the combinatorics of generators for certain groups and the combinatorics of Helly's 1913 theorem on convex sets. We use this connection to prove fixed point theorems for actions of these groups on nonpositively curved metric spaces. These results are encode d in a property that we introduce called ``property $FA_r$'', which reduces to Serre's property $FA$ when $r=1$. The method applies to $S$-arithmetic groups in higher $Q$-rank, to simplex reflection groups (including some non-arithmetic ones), and to higher rank Chevalley groups over polynomial and other rings (for example $SL_n(Z[x_1,..., x_d]), n>2$)." @default.
- W2146165986 created "2016-06-24" @default.
- W2146165986 creator A5031320327 @default.
- W2146165986 date "2008-06-10" @default.
- W2146165986 modified "2023-09-27" @default.
- W2146165986 title "Group actions and Helly's theorem" @default.
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