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A combination theorem for Anosov subgroups

  • Subhadip Dey
  • Michael Kapovich
  • Bernhard Leeb
Article
  • 22 Downloads

Abstract

We prove an analogue of Klein combination theorem for Anosov subgroups by using a local-to-global principle for Morse quasigeodesics.

List of symbols

\(\angle ^\xi _x(x_1,x_2)\)

\(\xi \)-Angle between \({\tau _{\mathrm {mod}}}\)-regular segments \(xx_1\) and \(xx_2\) (see Sect. 2.3)

\(\diamondsuit _\Theta \left( {x_1,x_2}\right) \)

\(\Theta \)-Diamond with tips at \(x_1\) and \(x_2\) (see Sect. 2.4)

\(\iota \)

The opposition involution (see Sect. 2.1)

\({\mathcal {N}}_{D}\left( {\cdot }\right) \)

Open D-neighborhood

\({\mathrm {ost}}\left( \tau \right) \)

Open star of \(\tau \) in the visual boundary (see Sect. 2.4)

\({\mathrm {st}}\left( \tau \right) \)

Star of \(\tau \) in the visual boundary (see Sect. 2.4)

\(V(x, {\mathrm {st}}_\Theta \left( \tau \right) )\)

\(\Theta \)-Cone asymptotic to \(\tau \) with tip at x (see Sect. 2.4)

Notes

Acknowledgements

The second author was partly supported by the NSF Grant DMS-16-04241, by KIAS (the Korea Institute for Advanced Study) through the KIAS scholar program, by a Simons Foundation Fellowship, Grant number 391602, and by Max Plank Institute for Mathematics in Bonn.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, DavisDavisUSA
  2. 2.Mathematisches InstitutUniversitaẗ MünchenMunichGermany

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