Open Questions: Noncommutative Geometry
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-
Noncommutative geometry
- Article from
Wikipedia.
-
Noncommutative Geometry
- "This site has been designed in order to offer to the community
of researchers in Noncommutative Geometry a center of resources
related to their work. Please read the Help file if you want
to provide information. The main purposes are to display Job
offers, conference announcements, and papers which can be of
interest for noncommutative geometers, from the prospective
to specialized levels. The information presented on this site
is provided by researchers themselves."
-
The Geometer of Particle Physics
- July 2006 Scientific American article.
"Alain Connes's noncommutative geometry offers an alternative
to string theory. In fact, being directly testable, it may be
better than string theory."
-
What are C*-algebras good for?
- Brief overview giving physical motivation without mathematical
details, by
John Baez.
-
Noncommutative Geometry and Quantum-Group Theory
- Very brief summary of the field, from a
tutorial conference
on the subject.
-
Geometry in Physics Tomorrow
- Slide presentation given by Isadore Singer at the
2001: A Spacetime Odyssey conference.
-
Nonabelian Gauge Theories on Noncommutative Spaces
- Slide presentation given by Bruno Zumino at the
2001: A Spacetime Odyssey conference.
Includes remarks on the Seiberg-Witten equations.
- Quantum Spaces and Their Noncommutative Topology
Joachim Cuntz
Notices of the AMS, September 2001, pp. 793-799
- Noncommutative geometry is based on the idea that the algebra
of functions on a topological space contains information about the
space. When the algebra is noncommutative, the result is noncommutative
geometry. The goal is to derive "topological" properties of a space
from its corresponding algebra of functions. The two fundamental
techniques available to do this are cyclic homology and
topological K-theory.
[Article in PDF format]
- Noncommutative Curves and Noncommutative Surfaces
J. T. Stafford; M. Van den Bergh
Bulletin of the AMS, April 2001, pp. 171-216
- Classical algebraic geometry is thoroughly entwined with the
theory of commutative rings. Nevertheless, a large part of the subject
can be generalized to the category of noncommutative rings, though not
in a straightforward manner.
[Abstract, references, downloadable text]
- Review of Noncommutative Geometry by Alain Connes
Vaughan Jones; Henri Moscovici
Notices of the AMS, August 1997, pp. 792-799
- Although presented as a book review, this is really an
expository paper on noncommutative geometry as developed by Connes.
The basic idea is that in some situations which have been treated
geometrically, the geometry itself can be better understood as
a study of a noncommutative algebra than as properties of a set
of points.
[Article in PDF format]
- Noncommutative Geometry
Andrew Lesniewski
Notices of the AMS, August 1997, pp. 800-805
- Quantum field theory is explicitly a geometrical approach
to the physical problems it deals with. This article explains
how Connes' noncommutative geometry can clarify a lot of modern
field theory.
[Article in PDF format]
- Review of Topics in non-commutative geometry by
Yuri I. Manin
Ivan Penkov
Bulletin of the AMS, July 1993, pp. 106-111
- The field of noncommutative geometry has recently been
dominated by Connes' work emphasizing C*
algebras, but its history goes back well before that. Manin's
book deals with many topics, but especially "supergeometry"
and quantum geometry (Hopf algebras).
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