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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 13th 2010

started a stub for projective space

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeDec 13th 2010

Added the first part of the proof that a $\mathbb{Z}$-grading on a commutative ring $R$ is the same as a $\mathbb{G}_m$-action on $Spec R$. (All a bit rough for the time being.)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 14th 2010
• (edited Dec 14th 2010)

added to projective space the remainder of the proof that $\mathbb{G}$-actions on $Spec R$ are equivalent to $\mathbb{Z}$-gradings of $R$.

(I guess I should move that elsewhere.)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 11th 2017
• (edited Jun 11th 2017)

I have spelled out how real and projective space become topological manifolds and smooth manifolds, here.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJun 12th 2017

I have filled in full details in the proof of the CW-structure at complex projective space. Then I copied this over also to Projective space – Examples – Real and complex projective space, so that the discussion there is now a self-contained proof of the manifold structure on real/complex projective space.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeAug 9th 2017

Among the list of elementary facts, the statement that $S^n \to \mathbb{R}P^n$ is locally trivial had been missing. For completeness, have now included statement and proof here.