Timeline for Defining a map into $S^1$ as an "angle" in a non simply connected domain
Current License: CC BY-SA 4.0
9 events
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| Mar 26, 2021 at 20:14 | comment | added | username | Hatcher's Algebraic Geometry is very useful (Pierre Albin's lectures on this book are very helpful) to understand your answer. Yet I think your answer doesn't answer my question, it describes what the space looks like, and why I cannot map to $\mathbb{R}$. I think the answer to my question is simply "yes" : there is a lift taking values in $\mathbb R/2\pi\mathbb Z$. | |
| Mar 26, 2021 at 20:04 | vote | accept | username | ||
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| Mar 12, 2021 at 15:05 | vote | accept | username | ||
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| Mar 12, 2021 at 12:31 | comment | added | Thomas Rot | You can have a look at Hatcher's algebraic topology book. This is discussed in the section on the fundamental group and covering spaces. | |
| Mar 12, 2021 at 12:30 | history | edited | Thomas Rot | CC BY-SA 4.0 |
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| Mar 12, 2021 at 12:30 | comment | added | Thomas Rot | in the case described the subgroup is $\mathbb Z$ itself. | |
| Mar 12, 2021 at 11:17 | comment | added | username | Thank you that is probably very helpful --that's not a language I am familiar with but I'll try to understand what it means. To take the example of $x/|x|$ in the domain described, which subgroups would it belong to? Is there such as thing as a lift from $\mathbb{R}/2\pi\mathbb{Z}$ to $S^1$? | |
| Mar 12, 2021 at 9:37 | history | answered | Thomas Rot | CC BY-SA 4.0 |