Lectures on coarse geometry

By J. Roe. 2003

753 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d1ead7c7bc5294a7658c280fba596873a3cd0860

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Index Theory of One Dimensional Quantum Walks and Cellular Automata (2009, background): “In this more general setup, neighborhood relations up to regroupings may be described in terms of coarse geometry [14], a theme we will not pursue here.”
Nonlinear spectral calculus and super-expanders (2012, background): “Nevertheless, this weak notion of embedding (much weaker than, say, bi-Lipschitz embeddability) has beautiful applications in geometry and group theory; see [18, 68, 12, 65, 20] and the references therein for examples of such applications.”
Uniform embeddability of relatively hyperbolic groups (2005, methodology): “Our gluing technique is inspired by the work of Bell and Dranishnikov on spaces of finite asymptotic dimension [3], [15], and by the work of Bell on Property A [2].”
The asymptotic dimension of a curve graph is finite (2005, methodology): “, Example (b)] and an explicit proof appears in Roe’s book [31].”
Property A, partial translation structures, and uniform embeddings in groups (2006, background): “4) are all equivalent. If moreover there is a partial translation structure which admits a free and globally controlled atlas then (1) through (7) are all equivalent. Proof. 1 =⇒ 2: This is proved in [11], Proposition11.41 and the equivalence 1 ⇔ 2 was proved in [13]. Here we give an alternative pro”
Mapping Surgery to Analysis II: Geometric Signatures (2004, background): “Remark 2.11. It is a technical question in functional analysis whether the processes of taking the -equivariant part and taking the norm limit can be interchanged in the definition above (see [ 19 ]).”
A notion of geometric complexity and its application to topological rigidity (2010, neutral): “(See [R2] for a direct argument.”
Geometric Group Theory (2018, methodology): “We refer the reader to [Aea91], [Bal95], [Bow91], [VSCC92], [Bow06a], [BH99], [CDP90], [Dav08], [Geo08], [GdlH90], [dlH00], [NY11], [Pap03], [Roe03], [Sap14], [Väi05] for the discussion of other parts of the theory.”
The nuclear dimension of C*-algebras (2009, background): “we explore a connection between the asymptotic dimension of a coarse space and the nuclear dimension of its uniform Roe algebra. Although both concepts may be deﬁned for arbitrary coarse spaces (c.f. [22]) we restrict ourselves to discrete metric spaces of bounded geometry, mostly for simplicity. Re”
Asymptotic dimension of relatively hyperbolic groups (2004, background): “For example, this is so for nilpotent groups, fundamental groups of finite graphs of groups where vertex groups have finite asymptotic dimension, hyperbolic groups, etc. (see [2, 3, 17 ] and references therein).”