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Filling functions of arithmetic groups

Leuzinger, Enrico; Young, Robert

Abstract:
The Dehn function and its higher-dimensional generalizations measure the difficulty of filling a sphere in a space by a ball. In nonpositively curved spaces, one can construct fillings using geodesics, but fillings become more complicated in subsets of nonpositively curved spaces, such as lattices in symmetric spaces. In this paper, we prove sharp filling inequalities for (arithmetic) lattices in higher rank semisimple Lie groups. When n is less than the rank of the associated symmetric space, we show that the n-dimensional filling volume function of the lattice grows at the same rate as that of the associated symmetric space, and when n is equal to the rank, we show that the n-dimensional filling volume function grows exponentially. This broadly generalizes a theorem of Lubotzky-Mozes-Raghunathan on length distortion in lattices and confirms conjectures of Thurston, Gromov, and Bux-Wortman.


Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2021
Sprache Englisch
Identifikator KITopen-ID: 1000135658
Umfang 49 S.
Nachgewiesen in arXiv
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