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A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

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''[https://youtu.be/Z7rd04KzLcg?t=8746 02:25:46]''<br>
''[https://youtu.be/Z7rd04KzLcg?t=8746 02:25:46]''<br>
So just to fix bundle notation, we let \(H\) be the structure group of a bundle \(P_H\) over a base space \(B\). We use \(\pi\) for the projection map. We've reserved the variation in the \(\pi\) orthography for the field content, and we try to use right principal actions. I'm terrible with left and right, but we do our best. We use \(H\) here, not \(\mathcal{G}\), because we want to reserve \(\mathcal{G}\) for the inhomogeneous extension of \(H\) once we move to function spaces.
So just to fix bundle notation, we let \(H\) be the structure group of a bundle \(P_H\) over a base space \(B\). We use \(\pi\) for the projection map. We've reserved the variation in the \(\pi\) orthography for the field content, and we try to use right principal actions. I'm terrible with left and right, but we do our best. We use \(H\) here, not \(G\), because we want to reserve \(G\) for the inhomogeneous extension of \(H\) once we move to function spaces.


[[File:GU Presentation Powerpoint Function Spaces Slide.png|center]]
[[File:GU Presentation Powerpoint Function Spaces Slide.png|center]]