Timeline for Probing a manifold with closed curves
Current License: CC BY-SA 3.0
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| Mar 15, 2013 at 15:34 | comment | added | Andrew Lobb | Thanks for all the upvotes, but I've realized that my argument is not correct. The space space $S$ is not necessarily a torus with some points identified but just some genus $g \geq 1$ surface with a finite number of points identified. It's fixable though. Orient $C_i$ and choose an oriented loop $P_i$ on $C_i$ with no self-intersections such that $P_1$ and $P_2$ intersect once. Then crushing the complement of a neighborhood of $P_1 \cup P_2$ gives an honest torus such that $C_1$ wraps once in one direction and $C_2$ wraps once in the other direction. | |
| Mar 14, 2013 at 21:28 | history | answered | Andrew Lobb | CC BY-SA 3.0 |