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Warped cones and spectral gaps


Authors: Piotr W. Nowak and Damian Sawicki
Journal: Proc. Amer. Math. Soc. 145 (2017), 817-823
MSC (2010): Primary 46B85; Secondary 37C85, 37A30
DOI: https://doi.org/10.1090/proc/13258
Published electronically: August 23, 2016
MathSciNet review: 3577880
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Abstract: We show that warped cones over actions with spectral gaps do not embed coarsely into large classes of Banach spaces. In particular, there exist warped cones over actions of the free group that do not embed coarsely into $ L_p$-spaces, and there are warped cones over discrete group actions that do not embed into any Banach space with non-trivial type.


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Additional Information

Piotr W. Nowak
Affiliation: Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland – and – Institute of Mathematics, University of Warsaw, Poland

Damian Sawicki
Affiliation: Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland

DOI: https://doi.org/10.1090/proc/13258
Received by editor(s): November 15, 2015
Received by editor(s) in revised form: March 27, 2016, and April 22, 2016
Published electronically: August 23, 2016
Additional Notes: Both authors were partially supported by Narodowe Centrum Nauki grant DEC-2013/10/EST1/00352. The second author was partially supported by Fundacja na rzecz Nauki Polskiej grant MISTRZ 5/2012 of Prof. Tadeusz Januszkiewicz
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 American Mathematical Society