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Results tagged with curves-and-surfaces
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user 1463
A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line
1
vote
A simple closed curve on a surface
This paper of Boggi gives an attractive algebraic characterisation of the conjugacy classes of the fundamental group $\pi_1\Sigma$ that are represented by simple closed curves. The idea is nice and ea …
- 25.2k
9
votes
How to detect a simple closed curve from the element in the fundamental group?
Various algorithms for determining whether a given conjugacy class contains a simple representative are given in the following papers.
Reinhart, Bruce L., 'Algorithms for Jordan curves on compact su …
- 25.2k
7
votes
Generate $\mathrm{Mod}(S_g)$ by two Dehn twists
This is addressed in §3.5.2 of Farb and Margalit's Primer on Mapping Class Groups. The subgroups of mapping class groups generated by two Dehn twists $T_a,T_b$ are one of:
$\mathbb{Z}$ if the curves …
- 25.2k
2
votes
Identifying a curve on a closed surface of genus 4
As mentioned in comments, your picture is not entirely accurate. But perhaps this is what you're looking for?
(Note that, if you had chosen a different gluing pattern for your once-punctured genus-tw …
- 25.2k