##  [Noncommutative Geometry](/noncommutative-geometry) 

  ##  [Noncommutative Geometry](https://puremath.quantumdictionary.io/noncommutative-geometry-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A framework that generalises geometric notions by replacing commutative algebras of functions on spaces with noncommutative algebras and operator‑theoretic structures, using tools such as spectral triples, K‑theory and cyclic cohomology to extract geometric data from algebraic/operator input.