Higher divergence for nilpotent Lie groups
HTML articles powered by AMS MathViewer
- by Moritz Gruber PDF
- Proc. Amer. Math. Soc. 148 (2020), 945-959 Request permission
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.References
- Aaron Abrams, Noel Brady, Pallavi Dani, Moon Duchin, and Robert Young, Pushing fillings in right-angled Artin groups, J. Lond. Math. Soc. (2) 87 (2013), no. 3, 663–688. MR 3073670, DOI 10.1112/jlms/jds064
- Noel Brady and Benson Farb, Filling-invariants at infinity for manifolds of nonpositive curvature, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3393–3405. MR 1608281, DOI 10.1090/S0002-9947-98-02317-4
- Herbert Federer and Wendell H. Fleming, Normal and integral currents, Ann. of Math. (2) 72 (1960), 458–520. MR 123260, DOI 10.2307/1970227
- Moritz Gruber, Filling invariants of stratified nilpotent Lie groups, Math. Z. (to appear), arXiv:1507.04871v3, 2015.
- Moritz Gruber, The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group, Adv. Geom. 19 (2019), no. 3, 415–420. MR 3982578, DOI 10.1515/advgeom-2019-0003
- Moritz Gruber, Large scale geometry of stratified nilpotent Lie groups, dissertation, Karlsruhe Institute of Technology, 2016.
- E. Leuzinger, Corank and asymptotic filling-invariants for symmetric spaces, Geom. Funct. Anal. 10 (2000), no. 4, 863–873. MR 1791143, DOI 10.1007/PL00001641
- Ben Warhurst, Jet spaces as nonrigid Carnot groups, J. Lie Theory 15 (2005), no. 1, 341–356. MR 2115247
- Stefan Wenger, Filling invariants at infinity and the Euclidean rank of Hadamard spaces, Int. Math. Res. Not. , posted on (2006), Art. ID 83090, 33. MR 2250014, DOI 10.1155/IMRN/2006/83090
- Joseph A. Wolf, Curvature in nilpotent Lie groups, Proc. Amer. Math. Soc. 15 (1964), 271–274. MR 162206, DOI 10.1090/S0002-9939-1964-0162206-7
- Robert Young, Filling inequalities for nilpotent groups through approximations, Groups Geom. Dyn. 7 (2013), no. 4, 977–1011. MR 3134033, DOI 10.4171/GGD/213
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
- Received by editor(s): August 14, 2018
- Received by editor(s) in revised form: October 3, 2018
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 945-959
- MSC (2010): Primary 20F65, 20F18
- DOI: https://doi.org/10.1090/proc/14759
- MathSciNet review: 4055925