Timeline for When does a submersion have connected fibers?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jan 3, 2013 at 14:31 | comment | added | Emerton | and so disconnected. Removing more points, or for example a curve, from $\mathbb R^2$, will give you examples with all kinds of behaviour. Regards, Matthew | |
| Jan 3, 2013 at 14:30 | comment | added | Emerton | Dear David, I don't know if you're still interested in this, but note that if we relax the condition that $F$ is a fibre-bundle, we pretty much lose all control. E.g. take $M$ to be an open subset of $\mathbb R^2$, take $N$ to be $\mathbb R$, thought of as (say) the $x$-axis of $\mathbb R^2$, and let $M \to N$ be the projection to the $x$-axis. Then the fibres of this map will be open subsets of $\mathbb R$, which can be pretty much anything. E.g. if $M$ is $\mathbb R^2$ minus one point, the fibres are $\mathbb R$ above all but one point, but above one point it is $\mathbb R$ minus a point | |
| Jun 24, 2010 at 10:59 | comment | added | David Carchedi | Also, it might be nice to do some class of examples which do not make $F$ into a fiber-bundle, so that the topologies of the fibers can vary. | |
| Jun 24, 2010 at 10:30 | comment | added | David Carchedi | Jason's answer and Boyarksy's comment are nice examples. Does anyone know of an example where the fibers are not compact? | |
| Jun 24, 2010 at 4:25 | answer | added | Jason DeVito - on hiatus | timeline score: 8 | |
| Jun 24, 2010 at 1:14 | history | asked | David Carchedi | CC BY-SA 2.5 |