the fundamental group of the immersed image of Klein bottle in $mathbb{R}^3$
$begingroup$
how to get the fundamental group of the immersed image of Klein bottle in $mathbb{R}^3$?
I just try to use the Van-Kampen theorem to prove it is $mathbb{Z}$. i am not sure.
if u know something about it, thanks for helping me .
algebraic-topology homotopy-theory
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
$endgroup$
add a comment |
$begingroup$
how to get the fundamental group of the immersed image of Klein bottle in $mathbb{R}^3$?
I just try to use the Van-Kampen theorem to prove it is $mathbb{Z}$. i am not sure.
if u know something about it, thanks for helping me .
algebraic-topology homotopy-theory
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
$endgroup$
add a comment |
$begingroup$
how to get the fundamental group of the immersed image of Klein bottle in $mathbb{R}^3$?
I just try to use the Van-Kampen theorem to prove it is $mathbb{Z}$. i am not sure.
if u know something about it, thanks for helping me .
algebraic-topology homotopy-theory
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
$endgroup$
how to get the fundamental group of the immersed image of Klein bottle in $mathbb{R}^3$?
I just try to use the Van-Kampen theorem to prove it is $mathbb{Z}$. i am not sure.
if u know something about it, thanks for helping me .
algebraic-topology homotopy-theory
algebraic-topology homotopy-theory
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
asked Dec 15 '18 at 5:09
yufeng luyufeng lu
353
353
add a comment |
add a comment |
1 Answer
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$begingroup$
by "collapsing subspace"(see Hatcher chapter 0) the immersed image is homotopy equivalence to the wedge sum of $S^1,S^1,S^2$.
so the fundamental group is $Z*Z$
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
$endgroup$
add a comment |
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$begingroup$
by "collapsing subspace"(see Hatcher chapter 0) the immersed image is homotopy equivalence to the wedge sum of $S^1,S^1,S^2$.
so the fundamental group is $Z*Z$
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
$endgroup$
add a comment |
$begingroup$
by "collapsing subspace"(see Hatcher chapter 0) the immersed image is homotopy equivalence to the wedge sum of $S^1,S^1,S^2$.
so the fundamental group is $Z*Z$
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
$endgroup$
add a comment |
$begingroup$
by "collapsing subspace"(see Hatcher chapter 0) the immersed image is homotopy equivalence to the wedge sum of $S^1,S^1,S^2$.
so the fundamental group is $Z*Z$
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
$endgroup$
by "collapsing subspace"(see Hatcher chapter 0) the immersed image is homotopy equivalence to the wedge sum of $S^1,S^1,S^2$.
so the fundamental group is $Z*Z$
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
answered Dec 16 '18 at 13:20
yufeng luyufeng lu
353
353
add a comment |
add a comment |
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