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Invariants for proper metric spaces and open Riemannian manifolds
Author(s) -
Eichhorn Jürgen
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310042
Subject(s) - mathematics , pure mathematics , homotopy , invariant (physics) , bounded function , homotopy category , cohomology , mathematical analysis , mathematical physics
We introduce uniform structures of proper metric spaces and open Riemannian manifolds, characterize their (arc) components, present new invariants like e.g. Lipschitz and Gromov–Hausdorff cohomology, specialize to uniform triangulations of manifolds and prove that the presence of a spectral gap above zero is a bounded homotopy invariant.