Mixing
Irregular covering of 2-holed torus $S_2$
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I need to find an irregular covering of the 2-holed torus. If a covering is regular, then $p_*(pi_1(E,e_0))$ is a normal subgroup of $pi_1(S_2,b_0)$, where $E$ denotes the covering space. So an irregular covering would not have this property. I was thinking if $E=S_2$ (which is just itself) is such a covering, but I don't know why or how to justify it. If the trivial covering is regular, then what would be an (easily understood) irregular covering of $S_2$? Thanks!
algebraic-topology covering-spaces
asked Jan 14 at 6:13
AlexAlex
757
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$begingroup$
I need to find an irregular covering of the 2-holed torus. If a covering is regular, then $p_*(pi_1(E,e_0))$ is a normal subgroup of $pi_1(S_2,b_0)$, where $E$ denotes the covering space. So an irregular covering would not have this property. I was thinking if $E=S_2$ (which is just itself) is such a covering, but I don't know why or how to justify it. If the trivial covering is regular, then what would be an (easily understood) irregular covering of $S_2$? Thanks!
algebraic-topology covering-spaces
asked Jan 14 at 6:13
AlexAlex
757
$endgroup$
add a comment |
$begingroup$
I need to find an irregular covering of the 2-holed torus. If a covering is regular, then $p_*(pi_1(E,e_0))$ is a normal subgroup of $pi_1(S_2,b_0)$, where $E$ denotes the covering space. So an irregular covering would not have this property. I was thinking if $E=S_2$ (which is just itself) is such a covering, but I don't know why or how to justify it. If the trivial covering is regular, then what would be an (easily understood) irregular covering of $S_2$? Thanks!
algebraic-topology covering-spaces
asked Jan 14 at 6:13
AlexAlex
757
$endgroup$
I need to find an irregular covering of the 2-holed torus. If a covering is regular, then $p_*(pi_1(E,e_0))$ is a normal subgroup of $pi_1(S_2,b_0)$, where $E$ denotes the covering space. So an irregular covering would not have this property. I was thinking if $E=S_2$ (which is just itself) is such a covering, but I don't know why or how to justify it. If the trivial covering is regular, then what would be an (easily understood) irregular covering of $S_2$? Thanks!
algebraic-topology covering-spaces
algebraic-topology covering-spaces
asked Jan 14 at 6:13
AlexAlex
757
asked Jan 14 at 6:13
AlexAlex
757
asked Jan 14 at 6:13
AlexAlex
757
asked Jan 14 at 6:13
AlexAlex
757
asked Jan 14 at 6:13
AlexAlex
757
757
add a comment |
add a comment |
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