Talk:Connection (principal bundle)

Latest comment: 7 years ago by Zhang875 in topic Ad and ad

Vertical space definition "Relation to Ehresmann connections"

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The definition given is Vp=Tp(Pπ(p)) but I'm confused by this since π(p) is in the base space but this gives the impression that it is in the total space P. The definition given in C. Isham Modern Differential Geometry for Physicists is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle V_p = \{\tau\in T_p P | \pi_* \tau = 0\}} — Preceding unsigned comment added by Gannektakazoink (talkcontribs) 17:12, 5 January 2013 (UTC)Reply

They coincide if Pπ(p) means the fiber π-1(π(p)) (which is a manifold) and Tp(Pπ(p)) means the tangent space to the fiber at the point p. In other words, vertical vectors are tangent vectors to the fibers, i.e., equivalence classes of curves in the fiber π-1(π(p)). Mgvongoeden (talk) 16:23, 29 May 2013 (UTC)Reply

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Please never abuse ad for Ad, please! Zhang875 (talk) 03:22, 21 November 2016 (UTC)Reply