Timeline for Twisted winding number
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 19, 2021 at 23:06 | vote | accept | Jack L. | ||
| Jan 19, 2021 at 17:15 | answer | added | Kostya_I | timeline score: 1 | |
| Jan 19, 2021 at 16:15 | comment | added | Jack L. | @Conrad: Many thanks for your comment. I am not necessarily presuming there’s a closed-form expression for every possible continuous function $\chi$; as may be easily observed, if $\chi$ is constant on $\gamma$, then the result is simply that constant times $n(\gamma,0)$. While I am more interested in the case $\chi(\cdot):=\langle\cdot\rangle^{-2}$, I thought perhaps there might be some results involving some non-trivial hypotheses on $\chi$ and incorporating my case of interest. | |
| Jan 19, 2021 at 16:07 | comment | added | Conrad | The general question is hopeless if $\chi$ arbitrary as you can take $1$ on an arc, $2$ on the complementary arc and smoothed out at ends and get arbitrary numbers depending on the arc (result is always positive for a circle oriented usually by parametrization) | |
| Jan 19, 2021 at 16:03 | comment | added | Conrad | I misunderstood the question and of course you are correct and I was wrong | |
| Jan 19, 2021 at 15:17 | history | edited | Jack L. | CC BY-SA 4.0 |
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| Jan 19, 2021 at 15:16 | comment | added | Jack L. | Ah yes, will correct appropriately. Thanks | |
| Jan 19, 2021 at 15:13 | comment | added | Will Sawin | Should $du/u$ be $dz/z$ here? | |
| Jan 19, 2021 at 15:04 | history | asked | Jack L. | CC BY-SA 4.0 |