Timeline for Homotopy type of a complex affine variety
Current License: CC BY-SA 3.0
4 events
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| Jan 20, 2017 at 16:01 | comment | added | Francesco Polizzi | When $X$ is any algebraic variety (in particular, any affine variety ), the aforementioned CW-compex is also finite. This implies that the fundamental group $\pi_1(X)$ and the homology and cohomology groups $H_i(X, \, \mathbb{Z})$, $H^i(X, \, \mathbb{Z})$ are all finitely generated. This is not true anymore fror an arbitrary smooth Stein space, for which the CW-complex can be infinite. Take for instance $$X=\{x \in \mathbb{C}\, | \, \sin x \neq 0 \}.$$ | |
| Jan 20, 2017 at 15:56 | vote | accept | CommunityBot | moved from User.Id=19475 by developer User.Id=69903 | |
| Jan 20, 2017 at 15:51 | history | edited | diverietti | CC BY-SA 3.0 |
added 172 characters in body
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| Jan 20, 2017 at 15:44 | history | answered | diverietti | CC BY-SA 3.0 |