Is there a biholomorphic map between a simply connected domain and non simply connected domain?
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Is there a biholomorphic map between a simply connected domain and non simply connected domain?
I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.
complex-analysis holomorphic-functions
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
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add a comment |
$begingroup$
Is there a biholomorphic map between a simply connected domain and non simply connected domain?
I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.
complex-analysis holomorphic-functions
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
$endgroup$
add a comment |
$begingroup$
Is there a biholomorphic map between a simply connected domain and non simply connected domain?
I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.
complex-analysis holomorphic-functions
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
$endgroup$
Is there a biholomorphic map between a simply connected domain and non simply connected domain?
I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.
complex-analysis holomorphic-functions
complex-analysis holomorphic-functions
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
edited Dec 7 '18 at 21:37
Saucy O'Path
6,1641627
6,1641627
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
asked Dec 7 '18 at 21:00
Cute BrownieCute Brownie
1,043417
1,043417
add a comment |
add a comment |
1 Answer
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Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
$endgroup$
add a comment |
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$begingroup$
Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
$endgroup$
add a comment |
$begingroup$
Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
$endgroup$
add a comment |
$begingroup$
Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
$endgroup$
Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
answered Dec 7 '18 at 21:03
Saucy O'PathSaucy O'Path
6,1641627
6,1641627
add a comment |
add a comment |
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