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  3. New Directions in Locally Compact Groups
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 February 2018
    08 February 2018
    ISBN:
    9781108332675
    9781108413121
    DOI:
    https://doi.org/10.1017/9781108332675
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.53kg, 366 Pages
    • Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    London Mathematical Society Lecture Note Series (447)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    London Mathematical Society Lecture Note Series (447)
    Information

    Book description

    This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.

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