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 Yearling
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Jul
1
asked When is a connected space, path connected?
Jul
1
asked A manifold is a covering space over its quotient by a group action
Jun
30
asked The lie bracket as a limit
Jun
25
accepted What is the differential of left translation?
Jun
24
awarded  Yearling
Jun
23
asked Which two knots are isotopic but not ambient isotopic?
Jun
17
accepted The fundamental vector fields of a principal bundle are vertical.
Jun
17
comment Motivation for the name “vertical subspace” in the context of fiber bundles.
I apologize, sir.
Jun
17
comment Motivation for the name “vertical subspace” in the context of fiber bundles.
Sure, but this identification forgets about the topology of the bundle and the way the tangent spaces sit against each other. Surely, the tangent bundle of a developable curve is not the union of its tangent lines as they sit in $R^n$. (The tangent line to a point of a curve is off course the gradient line of the curve, translated to this point.) @QiaochuYuan
Jun
17
comment Introductions to Ehresmann connections and Chern-Simons forms
Thank you again. Which review papers do you recommend for Chern-Simons forms?
Jun
17
comment Motivation for the name “vertical subspace” in the context of fiber bundles.
Thank you, Mr. @Yuan. I speak of the tangent bundle of the principle bundle. What do you call vertical spaces?
Jun
17
asked Motivation for the name “vertical subspace” in the context of fiber bundles.
Jun
16
asked The fundamental vector fields of a principal bundle are vertical.
Jun
16
comment What is the differential of left translation?
Yes, we need to work in a coordinate system in order to speak of the matrix of a linear operator.
Jun
16
comment Introductions to Ehresmann connections and Chern-Simons forms
I beg your pardon. What are some physics textbooks treating Chern-Simons theory?
Jun
16
comment What is the differential of left translation?
Thank you, sir. What did I do wrong that led me to a meaningless symbol?
Jun
16
revised What is the differential of left translation?
added 137 characters in body
Jun
16
comment Introductions to Ehresmann connections and Chern-Simons forms
Thank you, Bechira. I am sorry but Morita treats not the construction of the Chern-Simons form. Moreover I find no mention of Chern-Simons theory in Bott & Tu.
Jun
16
comment Introductions to Ehresmann connections and Chern-Simons forms
I am aware of Nakahara's book, and I will be reading it, @bechira.
Jun
16
comment What is a differentiable distribution on a manifold
Thank you, @JHance. How may we describe the tensor field $P$?