- #1
kakarukeys
- 190
- 0
There is one point I don't understand about G-torsor.
A Lie group G acts freely and transitively on a manifold F.
F x G -> F
(f, g) -> fg, f(g1g2) = (fg1)g2
is a smooth map.
fix an element f of F
then the map h
F -> G
fg -> g
is a homeomorphism.
I know h is open from the continuity of the map
{f} x G -> F
g -> fg
How to see h is continuous?
A Lie group G acts freely and transitively on a manifold F.
F x G -> F
(f, g) -> fg, f(g1g2) = (fg1)g2
is a smooth map.
fix an element f of F
then the map h
F -> G
fg -> g
is a homeomorphism.
I know h is open from the continuity of the map
{f} x G -> F
g -> fg
How to see h is continuous?
Last edited: