Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups

Bux K-U, Wortman K (2011)
Inventiones mathematicae 185(2): 395-419.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Let G(O(S)) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O(S)) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(O(S)) established in an earlier paper is sharp in this case. The geometric analysis underlying our result determines the connectivity properties of horospheres in thick Euclidean buildings.
Erscheinungsjahr
Zeitschriftentitel
Inventiones mathematicae
Band
185
Ausgabe
2
Seite(n)
395-419
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Bux K-U, Wortman K. Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. Inventiones mathematicae. 2011;185(2):395-419.
Bux, K. - U., & Wortman, K. (2011). Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. Inventiones mathematicae, 185(2), 395-419. doi:10.1007/s00222-011-0311-1
Bux, K. - U., and Wortman, K. (2011). Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. Inventiones mathematicae 185, 395-419.
Bux, K.-U., & Wortman, K., 2011. Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. Inventiones mathematicae, 185(2), p 395-419.
K.-U. Bux and K. Wortman, “Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups”, Inventiones mathematicae, vol. 185, 2011, pp. 395-419.
Bux, K.-U., Wortman, K.: Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. Inventiones mathematicae. 185, 395-419 (2011).
Bux, Kai-Uwe, and Wortman, Kevin. “Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups”. Inventiones mathematicae 185.2 (2011): 395-419.