Noncommutative Geometry
Connes' framework: spectral triples and cyclic cohomology.
Noncommutative Geometry. Connes’ framework: spectral triples and cyclic cohomology.
Foundations and canonical references
The standard treatments of noncommutative geometry approach the subject from complementary angles. Connes, Noncommutative Geometry (1994) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Gracia, Elements of Noncommutative Geometry (2001) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for noncommutative geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1994Noncommutative Geometryconnes-1994
- textbook · supporting · 2001Elements of Noncommutative Geometrygracia-bondia-2001, varilly-2001, figueroa-2001
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