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Diffeomorphism between the Klein bottle and the connected sum of projective spaces
The Next CEO of Stack OverflowAdding handles to a sphereWhat is $TmathbbS^2$?Tangent bundle of the projective space.How to embed Klein Bottle into $R^4$Immersions of the Klein BottleEmbedding of Klein bottle in $mathbbR^4$ and Klein bottle as quotientDiffeomorphism between the Cylinder and the Full-Twist Möbius StripExistence af a Frame on the Klein BottleWhy does the Gauss-Bonnet theorem seem to work for some square boundary identifications but not others?Difference between $[0, 1) times [0, 1)$ and the 2-torus
$begingroup$
I know that the Klein bottle is a $C^infty$ manifold (obtained as the quotient space of the action $(x,y) longrightarrow (x+1/2,-y)$ on the torus).
I have to find the diffeomorphim between the so obained Klein bottle and the connected sum of two projective spaces. I know it can be seen "cutting and pasting" the square which represents the Klein bottle $aba^-1b$, however I would like to find an esplicit diffeomormism, is that possible?
differential-geometry
edited Mar 18 at 20:29
Jean Marie
31k42255
asked Mar 18 at 19:58
dennisdennis
111
$endgroup$
add a comment |
$begingroup$
I know that the Klein bottle is a $C^infty$ manifold (obtained as the quotient space of the action $(x,y) longrightarrow (x+1/2,-y)$ on the torus).
I have to find the diffeomorphim between the so obained Klein bottle and the connected sum of two projective spaces. I know it can be seen "cutting and pasting" the square which represents the Klein bottle $aba^-1b$, however I would like to find an esplicit diffeomormism, is that possible?
differential-geometry
edited Mar 18 at 20:29
Jean Marie
31k42255
asked Mar 18 at 19:58
dennisdennis
111
$endgroup$
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
$endgroup$
– dantopa
Mar 18 at 20:04
$begingroup$
Capitalize the initial letter of a name like Klein (klein is small :) anglo-german pun)
$endgroup$
– Jean Marie
Mar 18 at 20:30
add a comment |
$begingroup$
I know that the Klein bottle is a $C^infty$ manifold (obtained as the quotient space of the action $(x,y) longrightarrow (x+1/2,-y)$ on the torus).
I have to find the diffeomorphim between the so obained Klein bottle and the connected sum of two projective spaces. I know it can be seen "cutting and pasting" the square which represents the Klein bottle $aba^-1b$, however I would like to find an esplicit diffeomormism, is that possible?
differential-geometry
edited Mar 18 at 20:29
Jean Marie
31k42255
asked Mar 18 at 19:58
dennisdennis
111
$endgroup$
I know that the Klein bottle is a $C^infty$ manifold (obtained as the quotient space of the action $(x,y) longrightarrow (x+1/2,-y)$ on the torus).
I have to find the diffeomorphim between the so obained Klein bottle and the connected sum of two projective spaces. I know it can be seen "cutting and pasting" the square which represents the Klein bottle $aba^-1b$, however I would like to find an esplicit diffeomormism, is that possible?
differential-geometry
differential-geometry
edited Mar 18 at 20:29
Jean Marie
31k42255
asked Mar 18 at 19:58
dennisdennis
111
edited Mar 18 at 20:29
Jean Marie
31k42255
asked Mar 18 at 19:58
dennisdennis
111
edited Mar 18 at 20:29
Jean Marie
31k42255
edited Mar 18 at 20:29
Jean Marie
31k42255
edited Mar 18 at 20:29
Jean Marie
31k42255
31k42255
asked Mar 18 at 19:58
dennisdennis
111
asked Mar 18 at 19:58
dennisdennis
111
asked Mar 18 at 19:58
dennisdennis
111
111
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
$endgroup$
– dantopa
Mar 18 at 20:04
$begingroup$
Capitalize the initial letter of a name like Klein (klein is small :) anglo-german pun)
$endgroup$
– Jean Marie
Mar 18 at 20:30
add a comment |
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
$endgroup$
– dantopa
Mar 18 at 20:04
$begingroup$
Capitalize the initial letter of a name like Klein (klein is small :) anglo-german pun)
$endgroup$
– Jean Marie
Mar 18 at 20:30
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
$endgroup$
– dantopa
Mar 18 at 20:04
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
$endgroup$
– dantopa
Mar 18 at 20:04
$begingroup$
Capitalize the initial letter of a name like Klein (klein is small :) anglo-german pun)
$endgroup$
– Jean Marie
Mar 18 at 20:30
$begingroup$
Capitalize the initial letter of a name like Klein (klein is small :) anglo-german pun)
$endgroup$
– Jean Marie
Mar 18 at 20:30
add a comment |
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$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer.
$endgroup$
– dantopa
Mar 18 at 20:04
$begingroup$
Capitalize the initial letter of a name like Klein (klein is small :) anglo-german pun)
$endgroup$
– Jean Marie
Mar 18 at 20:30