Prove that a function from R to the unit circle is a local diffeomorphism.(2.4.8 G&P)
$begingroup$
In order to prove the existence of the function $g$ in the question I want to proof that the following function is a diffeomorphism (I was told a hint that it is a diffeomorphism):
$$p(t) = (cos t, sin t)$$
But actually I see that this function is not 1-1, and what about its inverse how can I calculate it? could anyone help me in this?
The question I am speaking about is given below:
The question also has a part of its answer(without the proof of the existence of $g$) here:
Prove that $deg_2 (f) equiv q mod 2$
differential-topology intersection-theory
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
$endgroup$
add a comment |
$begingroup$
In order to prove the existence of the function $g$ in the question I want to proof that the following function is a diffeomorphism (I was told a hint that it is a diffeomorphism):
$$p(t) = (cos t, sin t)$$
But actually I see that this function is not 1-1, and what about its inverse how can I calculate it? could anyone help me in this?
The question I am speaking about is given below:
The question also has a part of its answer(without the proof of the existence of $g$) here:
Prove that $deg_2 (f) equiv q mod 2$
differential-topology intersection-theory
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
$endgroup$
$begingroup$
Do you know some covering maps theory, e.g. path lifting theorem?
$endgroup$
– positrón0802
Dec 10 '18 at 19:42
add a comment |
$begingroup$
In order to prove the existence of the function $g$ in the question I want to proof that the following function is a diffeomorphism (I was told a hint that it is a diffeomorphism):
$$p(t) = (cos t, sin t)$$
But actually I see that this function is not 1-1, and what about its inverse how can I calculate it? could anyone help me in this?
The question I am speaking about is given below:
The question also has a part of its answer(without the proof of the existence of $g$) here:
Prove that $deg_2 (f) equiv q mod 2$
differential-topology intersection-theory
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
$endgroup$
In order to prove the existence of the function $g$ in the question I want to proof that the following function is a diffeomorphism (I was told a hint that it is a diffeomorphism):
$$p(t) = (cos t, sin t)$$
But actually I see that this function is not 1-1, and what about its inverse how can I calculate it? could anyone help me in this?
The question I am speaking about is given below:
The question also has a part of its answer(without the proof of the existence of $g$) here:
Prove that $deg_2 (f) equiv q mod 2$
differential-topology intersection-theory
differential-topology intersection-theory
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
asked Dec 9 '18 at 23:23
hopefullyhopefully
253114
253114
$begingroup$
Do you know some covering maps theory, e.g. path lifting theorem?
$endgroup$
– positrón0802
Dec 10 '18 at 19:42
add a comment |
$begingroup$
Do you know some covering maps theory, e.g. path lifting theorem?
$endgroup$
– positrón0802
Dec 10 '18 at 19:42
$begingroup$
Do you know some covering maps theory, e.g. path lifting theorem?
$endgroup$
– positrón0802
Dec 10 '18 at 19:42
$begingroup$
Do you know some covering maps theory, e.g. path lifting theorem?
$endgroup$
– positrón0802
Dec 10 '18 at 19:42
add a comment |
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$begingroup$
Do you know some covering maps theory, e.g. path lifting theorem?
$endgroup$
– positrón0802
Dec 10 '18 at 19:42