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Visualization of the Hopf Bundle and the Dirac Connection
Author

Srdjan Vukmirovic
Organization: Faculty of Mathematics, Belgrade
URL: http://alas.matf.bg.ac.yu/~vsrdjan/
Revision date

2004-05-20
Description

Zonotile2 We visualize the Hopf bundle S1 -> S3 -> S2 by means of the stereographics projection S3 -> R3. Furthermore, we visualize the Dirac connection on this Hopf bundle. The horizontal lifts of a curve form the base space S2 to a total space S3, with respect to this connection, and are calculated and visualized. This is done as an appendix of the author's PhD thesis. The main part of the thesis shows different aspects of self-duality that can be seen as generalizations of the Dirac connection.

[Image created by hopf_eng.nb]
Subject

*Mathematics > Calculus and Analysis > Differential Geometry
Keywords

Hopf bundle, Dirac connection, connection, principal bundle, horizontal lift, holonomy
Related items

*Visualizing the Hopf Fibration   [in Articles]
URL

http://mathworld.wolfram.com/HopfMap.html
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hopf_eng.nb (31.7 KB) - Mathematica Notebook [for Mathematica 5.0]