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Results tagged with surfaces
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user 23571
A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.
6
votes
Accepted
Essential surfaces in the Exterior of Montesinos knots
, and he gave criteria for when such tubings produce incompressible surfaces. … From this one sees that closed incompressible surfaces exist in most cases. …
- 20k
5
votes
Accepted
Homotopy classes of homeomorphisms of a multiple pointed space
For more complicated surfaces such as closed surfaces of positive genus the map
$$
\pi_0{\rm Homeo^+}(M\ {\rm rel} \ P)\to \pi_0{\rm HomEq^+}(M\ {\rm rel} \ P)
$$
again has a nontrivial kernel as long …
- 20k
10
votes
Accepted
Handle decompositions using only 1-handles
The second statement ought to be in the literature somewhere but I don't know a reference so I'll give an argument.
The result can be rephrased in terms of graphs. Let $S$ be a compact connected sur …
- 20k
11
votes
Accepted
Homotopy versus path-homotopy on punctured surface
The special feature of $X$, a sphere with three or more punctures, that is being used here is that the space $E(X)$ of all homotopy equivalences $X\to X$ has $\pi_1 E(X)=0$. (Here we take the identity …
- 20k