Index Theory, Coarse Geometry, and Topology of Manifolds

1996 ◽  
Author(s):  
John Roe
Keyword(s):  
Index Theory ◽  
Coarse Geometry ◽  
And Topology ◽  
Topology Of Manifolds

Geometry and Topology of Manifolds

2020 ◽  
Author(s):  
Vicente Muñoz ◽  
Ángel González-Prieto ◽  
Juan Rojo
Keyword(s):  
And Topology ◽  
Topology Of Manifolds

scholarly journals On a theorem of Ambrose

2006 ◽  
Vol 81 (2) ◽  
pp. 149-152 ◽  
Author(s):  
David J. Wraith
Keyword(s):  
Ricci Curvature ◽  
Alternative Proof ◽  
And Topology ◽  
Riccati Inequality ◽  
Topology Of Manifolds

AbstractA Riccati inequality involving the Ricci curvature can be used to deduce many interesting results about the geometry and topology of manifolds. In this note we use it to present a short alternative proof to a theorem of Ambrose.

scholarly journals Coarse Geometry and Index Theory

2001 ◽  
Vol 144 ◽  
pp. 111-118
Author(s):  
Shingo Kamimura
Keyword(s):  
Index Theory ◽  
Coarse Geometry

scholarly journals Coarse amenability versus paracompactness

2014 ◽  
Vol 06 (01) ◽  
pp. 125-152 ◽  
Author(s):  
M. Cencelj ◽  
J. Dydak ◽  
A. Vavpetič
Keyword(s):  
Large Scale ◽  
Property A ◽  
Coarse Geometry ◽  
Easy Proof ◽  
And Topology ◽  
Large Scale Geometry ◽  
Nontrivial Group ◽  
Paracompact Spaces

Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was later strengthened to be the large scale analog of paracompact spaces using partitions of unity. In this paper we go deeper into divulging analogies between coarse amenability and paracompactness. In particular, we define a new coarse analog of paracompactness modeled on the defining characteristics of expanders. That analog gives an easy proof of three categories of spaces being coarsely non-amenable: expander sequences, graph spaces with girth approaching infinity, and unions of powers of a finite nontrivial group.

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