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Coarse Geometry of Topological Groups (Hardcover, New Ed)
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Coarse Geometry of Topological Groups (Hardcover, New Ed)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 17 working days
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This book provides a general framework for doing geometric group
theory for many non-locally-compact topological transformation
groups that arise in mathematical practice, including homeomorphism
and diffeomorphism groups of manifolds, isometry groups of
separable metric spaces and automorphism groups of countable
structures. Using Roe's framework of coarse structures and spaces,
the author defines a natural coarse geometric structure on all
topological groups. This structure is accessible to investigation,
especially in the case of Polish groups, and often has an explicit
description, generalising well-known structures in familiar cases
including finitely generated discrete groups, compactly generated
locally compact groups and Banach spaces. In most cases, the coarse
geometric structure is metrisable and may even be refined to a
canonical quasimetric structure on the group. The book contains
many worked examples and sufficient introductory material to be
accessible to beginning graduate students. An appendix outlines
several open problems in this young and rich theory.
General
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