In metric geometry, asymptotic dimension of a metric space is a large-scale analog of Lebesgue covering dimension. The notion of asymptotic dimension was introduced by Mikhail Gromov in his 1993 monograph Asymptotic invariants of infinite groups[1] in the context of geometric group theory, as a quasi-isometry invariant of finitely generated groups. As shown by Guoliang Yu, finitely generated groups of finite homotopy type with finite asymptotic dimension satisfy the Novikov conjecture.[2] Asymptotic dimension has important applications in geometric analysis and index theory.
- ^ Gromov, Mikhael (1993). "Asymptotic Invariants of Infinite Groups". Geometric Group Theory. London Mathematical Society Lecture Note Series. Vol. 2. Cambridge University Press. ISBN 978-0-521-44680-8.
- ^ Cite error: The named reference
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