Timeline for A topological property of flat morphisms
Current License: CC BY-SA 3.0
8 events
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| Mar 23, 2017 at 10:06 | comment | added | Ariyan Javanpeykar | @R.vanDobbendeBruyn Whoops. You're right, I misread the question. | |
| Mar 22, 2017 at 15:34 | comment | added | R. van Dobben de Bruyn | By the rank theorem (of real manifolds), on the smooth locus the map is locally given by some coordinate projection. Then the question becomes how the $\varepsilon$-balls behave with respect to projection. There are certainly open sets which do not have this property w.r.t. a coordinate projection, but the question is about (small!) metric balls. I think for $x \in U$ it might not be too bad, but when $x \not \in U$ this approach doesn't really help. | |
| Mar 22, 2017 at 15:27 | comment | added | R. van Dobben de Bruyn | @Ariyan: the OP's question is (analytic) local on $X$ (not $Y$!). Without properness of the map, in general the Betti numbers are certainly not constant over $U$. | |
| Mar 22, 2017 at 13:04 | comment | added | Ariyan Javanpeykar | The Betti numbers are constant over $U$. Doesn't that imply what you want? | |
| Mar 22, 2017 at 11:36 | history | edited | asv | CC BY-SA 3.0 |
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| Mar 22, 2017 at 11:24 | history | edited | asv | CC BY-SA 3.0 |
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| Mar 22, 2017 at 10:59 | history | edited | asv | CC BY-SA 3.0 |
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| Mar 22, 2017 at 9:57 | history | asked | asv | CC BY-SA 3.0 |