What are the necessary background topics for NCG?

  • Thread starter Thread starter ehrenfest
  • Start date Start date
  • Tags Tags
    Geometry
Click For Summary

Discussion Overview

The discussion focuses on the necessary background topics required to study Noncommutative Geometry (NCG) and related fields such as Lie groups. Participants explore various mathematical prerequisites and foundational subjects that may be beneficial for understanding these advanced topics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that Real Analysis, Complex Analysis, Topology, and Algebra are essential prerequisites for studying NCG, referencing specific texts as benchmarks.
  • Another participant proposes that algebraic geometry, homology, cohomology, and k-theory should also be considered as important background topics for NCG.
  • There is a separate inquiry about the prerequisites for studying Lie groups, with a participant noting the necessity of knowledge in both algebra and differential geometry due to the nature of Lie groups as differentiable manifolds.

Areas of Agreement / Disagreement

Participants present multiple viewpoints on the prerequisites for NCG and Lie groups, indicating that there is no consensus on a definitive list of necessary topics.

Contextual Notes

Some prerequisites mentioned may depend on the specific focus within NCG or Lie groups, and the discussion does not resolve the extent to which each topic is necessary or sufficient.

ehrenfest
Messages
2,001
Reaction score
1
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".
 
Physics news on Phys.org
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.
 
Last edited by a moderator:
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.
 

Similar threads

Replies
41
Views
8K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 9 ·
Replies
9
Views
2K