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The direction of an automorphism of a totally disconnected locally compact group

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Abstract

We describe the asymptotic behavior of automorphisms of totally disconnected locally compact groups in terms of a set of `directions' which comes equipped with a natural pseudo-metric. The structure at infinity obtained by completing the induced metric quotient space of the set of directions recovers familiar objects such as: the set of ends of the tree for the group of inner automorphisms of the group of isometries of a regular locally finite tree; and the spherical Bruhat-Tits building for the group of inner automorphisms of the set of rational points of a semisimple group over a local field.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Building V, Callaghan, NSW, 2308, Australia

    Udo Baumgartner & George A. Willis

Authors
  1. Udo Baumgartner
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  2. George A. Willis
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Correspondence to Udo Baumgartner.

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Research supported by A.R.C. Grant DP0208137.

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Baumgartner, U., Willis, G. The direction of an automorphism of a totally disconnected locally compact group. Math. Z. 252, 393–428 (2006). https://doi.org/10.1007/s00209-005-0861-2

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  • DOI: https://doi.org/10.1007/s00209-005-0861-2

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