What are the necessary background topics for NCG?

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To study Noncommutative Geometry (NCG), a solid foundation in several advanced mathematical subjects is essential. Key prerequisites include Real Analysis, specifically at the level of Rudin's "Principles of Mathematical Analysis," and Complex Analysis, ideally using Marsden's "Basic Complex Analysis." A strong understanding of Topology, as presented in Munkres' work, is also necessary. Additionally, knowledge of Algebra, particularly Fraleigh's "An Introduction to Abstract Algebra," is crucial. Familiarity with algebraic geometry, homology, cohomology, and k-theory, as discussed in Connes' texts, further enhances preparedness for NCG.For those interested in studying Lie groups, it is important to have a grasp of both algebra and differential geometry, as Lie groups combine elements of group theory with differentiable manifolds.
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What are the prerequisites to study NCG?

I know Real Analysis at the level of Rudin's "Principles of Mathematical Analysis", Complex Analysis at the level of Marsden's "Basic Complex Analysis," Topology at the level of Munkres, Algebra at the level of Fraleigh's "An Introduction to Abstract Algebra".
 
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Probably algebraic geometry, homology and cohomology as pre-pre-requisites.

You can also see some remarks about k-theory in Connes text. So I guess that's another prerequisite.
 
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OK. Guess I should wait a bit.
 
What are the prerequisites to study Lie groups?
 
ehrenfest said:
What are the prerequisites to study Lie groups?

Lie group = group + differentiable manifold, hence knowledge in both algebra and differential geometry is needed.
 

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