Lie group map whose differential is an isomorphism is a covering map
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While trying to read the proof in Fulton and Harris of their “Second Principle,” I ran across something that I do not understand. They seem to claim that if $f: Grightarrow H$ is a map of Lie groups whose differential $(df)_e: mathfrak{g}rightarrowmathfrak{h}$ is an isomorphism, then f is a covering map. Can anyone provide a proof or a reference?
lie-groups lie-algebras covering-spaces tangent-spaces
asked Jan 16 at 8:21
user320832user320832
1707
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add a comment |
$begingroup$
While trying to read the proof in Fulton and Harris of their “Second Principle,” I ran across something that I do not understand. They seem to claim that if $f: Grightarrow H$ is a map of Lie groups whose differential $(df)_e: mathfrak{g}rightarrowmathfrak{h}$ is an isomorphism, then f is a covering map. Can anyone provide a proof or a reference?
lie-groups lie-algebras covering-spaces tangent-spaces
asked Jan 16 at 8:21
user320832user320832
1707
$endgroup$
$begingroup$
Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map?
$endgroup$
– Praphulla Koushik
Jan 18 at 17:55
add a comment |
$begingroup$
While trying to read the proof in Fulton and Harris of their “Second Principle,” I ran across something that I do not understand. They seem to claim that if $f: Grightarrow H$ is a map of Lie groups whose differential $(df)_e: mathfrak{g}rightarrowmathfrak{h}$ is an isomorphism, then f is a covering map. Can anyone provide a proof or a reference?
lie-groups lie-algebras covering-spaces tangent-spaces
asked Jan 16 at 8:21
user320832user320832
1707
$endgroup$
While trying to read the proof in Fulton and Harris of their “Second Principle,” I ran across something that I do not understand. They seem to claim that if $f: Grightarrow H$ is a map of Lie groups whose differential $(df)_e: mathfrak{g}rightarrowmathfrak{h}$ is an isomorphism, then f is a covering map. Can anyone provide a proof or a reference?
lie-groups lie-algebras covering-spaces tangent-spaces
lie-groups lie-algebras covering-spaces tangent-spaces
asked Jan 16 at 8:21
user320832user320832
1707
asked Jan 16 at 8:21
user320832user320832
1707
asked Jan 16 at 8:21
user320832user320832
1707
asked Jan 16 at 8:21
user320832user320832
1707
asked Jan 16 at 8:21
user320832user320832
1707
1707
$begingroup$
Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map?
$endgroup$
– Praphulla Koushik
Jan 18 at 17:55
add a comment |
$begingroup$
Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map?
$endgroup$
– Praphulla Koushik
Jan 18 at 17:55
$begingroup$
Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map?
$endgroup$
– Praphulla Koushik
Jan 18 at 17:55
$begingroup$
Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map?
$endgroup$
– Praphulla Koushik
Jan 18 at 17:55
add a comment |
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$begingroup$
Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map?
$endgroup$
– Praphulla Koushik
Jan 18 at 17:55