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Lipschitz 1-connectedness for Some Solvable Lie Groups

Part of: Lie groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 January 2019

David Bruce Cohen
David Bruce Cohen*
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA Email: davidbrucecohen@gmail.com
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Abstract

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A space X is said to be Lipschitz 1-connected if every Lipschitz loop 𝛾 : S1 → X bounds a O (Lip(𝛾))-Lipschitz disk f : D2 → X. A Lipschitz 1-connected space admits a quadratic isoperimetric inequality, but it is unknown whether the converse is true. Cornulier and Tessera showed that certain solvable Lie groups have quadratic isoperimetric inequalities, and we extend their result to show that these groups are Lipschitz 1-connected.

Keywords

Dehn functionsolvable groupLipschitz 1-connectedness

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 22E25: Nilpotent and solvable Lie groups
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 3 , June 2019 , pp. 533 - 555
Copyright
© Canadian Mathematical Society 2018 

Footnotes

This work was supported by NSF award 1148609.

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