I would like some intuition for the horizontal bundle, could someone please make a drawing for me? I found a nice pucture here https://commons.m.wikimedia.org/wiki/File:Ehresmann_connection.png#mw-jump-to-license so I kind of understand the vertical bundle (it seems to be the paths in the total space which are mapped to a point in the base space), but I got stuck at understanding what the horizontal bundle is (some kind of complement is all I got). I did not understand what the red squares in the image represented in terms of paths. Does horizontal bundles need to have paths that are in a plane in the total space somehow ? How are they mapped into the base space (and fiber)?
2026-03-30 10:07:30.1774865250
Horizontal bundle visualization?
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