Gentle introduction to fibre bundles and gauge connections

Question

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.

Comments

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

Answer 1

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 ).

Answer 2

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

Comments

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

Answer 3

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

Answer 4

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

Comments

Thanks, this looks nice too.

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

Answer 5

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