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Gentle introduction to fibre bundles and gauge connections

+ 5 like - 0 dislike
1952 views

To better understand papers like this for example, which makes heavy use of fibre bundles and gauge connections to represent gauge fields, I am looking for a nice introduction to this topic.

The only thing I have read so far is the corresponding chapter 15 of Roger Penrose's "Road to Reality".

I do not want to read a whole book, I am rather thinking about an appropriate introductory paper, lecture notes, or a tutorial.

asked Feb 6, 2013 in Resources and References by Dilaton (4,175 points) [ revision history ]
recategorized Apr 24, 2014 by dimension10
I have noted that this question is related and looks similar, but the answers do not contain what I am looking for.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Dilaton

5 Answers

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A good math book about (mostly vector) bundles and connections is

C.H. Taubes, Differential geometry. Bundles, connections, metrics and curvature ( http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199605880.001.0001/acprof-9780199605880 ).
answered Jun 15, 2015 by just-learning (95 points) [ no revision ]
+ 2 like - 0 dislike

for fiber bundles,you may look into novikov's modern geometry part 2. it gives nice explanation and a good place to do learn some "real geometry"

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user K.Ghosh
answered Feb 6, 2013 by K.Ghosh (0 points) [ no revision ]
Thanks for this hint, I hope you do not mind that I inserted a link to the book.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Dilaton
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You can find the definition of a fiber bundle and some examples on pp 376-379 of Hatcher's online book Algebraic Topology. You might also consult "Fiber Bundles," chapter 4 of Lecture Notes in Algebraic Topology, by Davis-Kirk. A fast introduction to connections and curvature can be found here. In the case of surfaces, chapter 3 of these lecture notes might be useful to you.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Neal
answered Feb 6, 2013 by Neal (0 points) [ no revision ]
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For a 'physicsy' viewpoint, checkout "Geometry of Physics" by Frankel.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user nonlinearism
answered Feb 6, 2013 by nonlinearism (0 points) [ no revision ]
Thanks, this looks nice too.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Dilaton
+ 1 like - 0 dislike

I do not know what are gauge connections. However for connections on bundles, a "lecture note" reference is J.-L. Koszul's Lectures on Fibre Bundles and Differential Geometry.

This post imported from StackExchange Mathematics at 2014-03-09 16:08 (UCT), posted by SE-user Doldrums
answered Oct 29, 2013 by Doldrums (0 points) [ no revision ]

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