Timeline for Contractible real analytic varieties
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| May 23, 2023 at 11:18 | vote | accept | Brian Lins | ||
| May 13, 2023 at 17:36 | comment | added | Moishe Kohan | I find it very surprising that somebody can ask a question about contractible spaces and not be familiar with basics of homology. I also have no idea how one can justify the sentence "This is certainly true if $V$ is a compact real analytic manifold (without boundary)" (from your post) without using homology. | |
| May 12, 2023 at 15:36 | comment | added | Moishe Kohan | Did you understand the answer? | |
| May 10, 2023 at 2:35 | answer | added | Moishe Kohan | timeline score: 4 | |
| May 9, 2023 at 16:16 | comment | added | Brian Lins | Yes, I guess my question could be generalized by only requiring the analytic function $f$ be defined on an open subset of $\mathbb{R}^n$ and then assuming that the variety $V$ defined by $f$ is contractible and compact. | |
| May 9, 2023 at 15:05 | comment | added | Z. M | In your edit, you seem to impose that the function is globally defined, but the usual definition of complex analytic sets is defined locally being a zero set of local analytic functions. | |
| May 9, 2023 at 14:58 | comment | added | Brian Lins | Thanks, I've edited the question. | |
| May 9, 2023 at 14:57 | history | edited | Brian Lins | CC BY-SA 4.0 |
added 123 characters in body
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| May 9, 2023 at 14:55 | comment | added | Moishe Kohan | You should update your question accordingly (since there are inequivalent definitions in the literature). | |
| May 9, 2023 at 14:46 | comment | added | Brian Lins | A real analytic variety is the set of zeros of one or more real analytic functions (in this case, real-valued functions that are real analytic on $\mathbb{R}^n$). Of course, a real analytic variety that is defined by more than one real analytic function $f_1, f_2, \ldots, f_k$ can be expressed as the zero set of $f_1^2 + f_2^2 + \ldots f_k^2$. | |
| May 9, 2023 at 13:47 | comment | added | Moishe Kohan | What is your definition of a "real analytic variety in $R^n$?" | |
| May 9, 2023 at 13:25 | answer | added | Francesco Polizzi | timeline score: 2 | |
| May 9, 2023 at 12:11 | history | asked | Brian Lins | CC BY-SA 4.0 |