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Lipschitz 1-connectedness for Some Solvable Lie Groups

  • David Bruce Cohen (a1)
Abstract

A space X is said to be Lipschitz 1-connected if every Lipschitz loop 𝛾 : S1X bounds a O (Lip(𝛾))-Lipschitz disk f : D2X. 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.

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This work was supported by NSF award 1148609.

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[1] Abels, Herbert, Finite presentability of S-arithmetic groups. In: Compact presentability of solvable groups. Lecture Notes in Mathematics, 1261. Springer-Verlag, Berlin, 1985. https://doi.org/10.1007/BFb0079708.
[2] Borel, Armand, Linear algebraic groups. Second edition. Graduate Texts in Mathematics, 126. Springer-Verlag, New York, 1991.
[3] Bridson, Martin R. and Haefliger, André, Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften, 319. Springer-Verlag, Berlin, 1999. https://doi.org/10.1007/978-3-662-12494-9.
[4] Cornulier, Yves and Tessera, Romain, Geometric presentations of Lie groups and their Dehn functions . Publ. Math. Inst. Hautes Études Sci. 125(2017), 79219. https://doi.org/10.1007/s10240-016-0087-3.
[5] Epstein, David, Paterson, Mike S., Cannon, James W., Holt, Derek F., Levy, Silvio V, and Thurston, William P, Word processing in groups. Jones and Bartlett, Boston, MA, 1992.
[6] Gromov, Mikhail, Asymptotic invariants of infinite groups. In: Geometric group theory. Vol. 2, London Math. Soc. Lecture Notes Series, 182, Cambridge University Press, Cambridge, 1993.
[7] Kobayashi, Shoshichi and Nomizu, Katsumi, Foundations of differential geometry. Volume 1. Interscience Publishers, New York, 1963.
[8] Lytchak, Alexander, Wenger, Stefan, and Young, Robert, Dehn functions and Hölder extensions in asymptotic cones. arxiv:1608.00082, 2016.
[9] Mitsuishi, Ayato and Yamaguchi, Takao, Locally Lipschitz contractibility of Alexandrov spaces and its applications . Pacific J. Math. 270(2014), no. 2, 393421. https://doi.org/10.2140/pjm.2014.270.393.
[10] Young, Robert, The Dehn function of SL (n, Z) . Ann. of Math. 177(2013), no. 3, 9691027. https://doi.org/10.4007/annals.2013.177.3.4.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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