Pontryagin densities and Chern-Simons form

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Discussion Overview

The discussion revolves around the definition and formulation of Pontryagin densities in the context of 4-dimensional spacetime and their relation to arbitrary groups. Participants explore the implications of these densities and inquire about their formulas, particularly for larger groups.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that Pontryagin densities are defined in even-dimensional spaces and seeks clarification on their formula for arbitrary groups in 4-dimensional spacetime.
  • Another participant states that there are only two independent combinations of Pontryagin classes in 4 dimensions: the Euler class and the Hirzebruch signature, expressing uncertainty about the original question's intent.
  • A participant critiques the initial poster for not providing sufficient context or references in their opening post, suggesting that this may hinder the quality of responses.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the original question regarding Pontryagin densities, and there is a mix of responses that include clarification, critique, and uncertainty.

Contextual Notes

The discussion highlights the need for clearer definitions and context when posing questions related to advanced mathematical concepts, as well as the potential for misunderstanding without adequate background information.

shereen1
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Dear All
It is known that pontryagin densities are defined in even dimension space, let's say i am concerned with 4 dim space time. We also have a certain group G. What is the formula of pontryagin densities for arbitrary group? Larger group?
 
There are only two independent (combinations of) Pontrjagin classes in 4 dimensions: the Euler class and the Hirzebruch signature.

I'm not sure what the rest of your question is asking.
 
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Shereen,

if you expect decent answers you should spend more time on your opening posts, giving references and contexts. I think I gave that advice before.
 
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haushofer said:
Shereen,

if you expect decent answers you should spend more time on your opening posts, giving references and contexts. I think I gave that advice before.

sure i will.
Thank you
 

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