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Higher divergence for nilpotent Lie groups


Author: Moritz Gruber
Journal: Proc. Amer. Math. Soc. 148 (2020), 945-959
MSC (2010): Primary 20F65, 20F18
DOI: https://doi.org/10.1090/proc/14759
Published electronically: August 28, 2019
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Abstract: The higher divergence of a metric space describes its isoperimetric behaviour at infinity. It is closely related to the higher-dimensional Dehn functions but has more requirements to the fillings. We prove that these additional requirements do not have an essential impact for many nilpotent Lie groups. As a corollary, we obtain the higher divergence of the Heisenberg groups in all dimensions.


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Additional Information

Moritz Gruber
Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012
Email: moritz.gruber@nyu.edu

DOI: https://doi.org/10.1090/proc/14759
Received by editor(s): August 14, 2018
Received by editor(s) in revised form: October 3, 2018, June 10, 2019, and June 30, 2019
Published electronically: August 28, 2019
Additional Notes: The author was supported by the German Research Foundation (DFG) grant GR 5203/1-1
Communicated by: Kenneth Bromberg
Article copyright: © Copyright 2019 American Mathematical Society