Timeline for Covering maps in real life that can be demonstrated to students
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2013 at 15:02 | comment | added | Lee Mosher | Counterexamples which just barely miss being examples can often enhance understanding. Furthermore this example, while not a covering space in the usual topological category, is indeed a covering space in the orbifold category, and it can be used to exhibit the isomorphism between the infinite dihedral group (the deck transformation group of the orbifold universal covering space) with the fundamental group of the orbifold $[0,1] \times \mathbb{R}$ with mirror reflectors on the boundary. | |
| Dec 6, 2012 at 16:00 | comment | added | Hiro Lee Tanaka | Mark, I think Guntram's covering map wasn't to the folded sheet of paper, but to a single doll holding its own hand. But I agree--otherwise this is not at all an example of a covering map: It wouldn't even be a local homeomorphism. (Showing such an example to students could really hurt their understanding.) | |
| Dec 6, 2012 at 7:01 | comment | added | Mark Grant | Nice example! I think this covering is branched though (as the fiber at a point on the doll's foot, say, has twice as many points as the fiber at a point right between her eyes). | |
| Dec 6, 2012 at 6:23 | history | answered | Guntram | CC BY-SA 3.0 |