- #1

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I was thinking of sending the line that joins two antipodal points on the boundary of this ball, is this right, or should I be looking for something else?

Thanks.

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- Thread starter MathematicalPhysicist
- Start date

For the 2 sphere - CP1 - just map the boundary of the disk to the south pole. Generalize this.I don't understand how does this maps D^2n onto CP^n?I mean CP^n is homeomorphic to a sphere of S^{2n+1}, so if I map S^2n to a point at the south pole of S^2n, I don't see how does this mapping cover all of S^{2n+1} ~ CP^n?What's a "sphere of S^{2n+1}"? Anyway, CP^n is definitely not a sphere for n>1. It is obtained from quotienting S^{2n+1}f

- #1

- 4,699

- 369

I was thinking of sending the line that joins two antipodal points on the boundary of this ball, is this right, or should I be looking for something else?

Thanks.

- #2

Science Advisor

Gold Member

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I was thinking of sending the line that joins two antipodal points on the boundary of this ball, is this right, or should I be looking for something else?

Thanks.

For the 2 sphere - CP1 - just map the boundary of the disk to the south pole. Generalize this.

- #3

- 4,699

- 369

I don't understand how does this maps D^2n onto CP^n?

- #4

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- 369

- #5

Science Advisor

Homework Helper

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In particular, CP^0 = {pt} and CP^1=S^2. Why? Because there is a homeomorphism between the open set U:={[z0:z1]| z0 not equal to 0} and

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