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Geometric representation of small-rank totally disconnected groups

Title
Geometric representation of small-rank totally disconnected groups
Funding
ARC | Discovery Projects
Contract (GA) number
DP0556017
Start Date
2005/01/01
End Date
2007/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0556017

 

  • Geometric characterization of flat groups of automorphisms

    Baumgartner, Udo; Schlichting, Günter; Willis, George A. (2008)
    Projects: ARC | Geometric representation of small-rank totally disconnected groups (DP0556017)
    If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In this note we prove the following partial converse: Assume that G is a totally disconnected, locally compact group such that B(G) is a proper metric space and let H be a group of automorphisms of G such that some (equivalently every) orbit of H in B(G) is q...

    Contraction groups in complete Kac-Moody groups

    Baumgartner , Udo; Ramagge , Jacqui; Remy , Bertrand (2007)
    Projects: ARC | Geometric representation of small-rank totally disconnected groups (DP0556017)
    Let $G$ be an abstract Kac-Moody group over a finite field and $\overline{G}$ be the closure of the image of $G$ in the automorphism group of its positive building. We show that if the Dynkin diagram associated to $G$ is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in $\overline{G}$ which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

    A note concerning a tidying procedure and contraction groups in non-metrizable, totally disconnected groups

    In a 2004 article, Udo Baumgartner and George Willis used ideas from the structure theory of totally disconnected, locally compact groups to achieve a better understanding of the contraction group U_f associated with an automorphism f of such a group G, assuming that G is metrizable. (Recall that U_f consists of all group elements x such that f^n(x) tends to the identity element as n tends to infinity). Recently, Wojciech Jaworski showed that the main technical tool of the latter article rema...

    Invariant manifolds for analytic dynamical systems over ultrametric fields

    We give an exposition of the theory of invariant manifolds around a fixed point, in the case of time-discrete, analytic dynamical systems over a complete ultrametric field K. Typically, we consider an analytic manifold M modelled on an ultrametric Banach space over K, an analytic self-map f of M, and a fixed point p of f. Under suitable conditions on the tangent map of f at p, we construct a centre-stable manifold, a centre manifold, respectively, an r-stable manifold around p, for a given po...
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