All Questions
11 questions
0
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Let K be a compact set in a surface, U component of S-K, K'=S-U. K has finitely many components. Does every component of K' contains a component of K? [closed]
Let $S$ be a compact connected surface. Let $K$ be a compact subset of $S$ and suppose that $K$ has a finite number of connected components.
Let $U$ be a connected component of $S \setminus K$ and ...
0
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2
answers
348
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If a graph embedded on a surface is divided by a curve into a right and left that do not intersect can it be embedded on a surface of smaller genus?
Suppose we have a graph $G$ embedded on a (smooth, orientable etc) surface $Q$. Suppose there is a cycle $C$ of $G$ such that
$C$ does not separate our surface $Q$ into two connected regions and ...
- 111
1
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1
answer
177
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Identifying a curve on a closed surface of genus 4
The notation is the one used in the attached picture.
Take a closed, orientable surface $\Sigma_4$ of genus $4$, obtained as the identification space of a polygon with $16$ sides in the usual way. The ...
- 66.3k
1
vote
0
answers
143
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End space of non-compact 2-manifolds described with proper rays
I am wondering if the classification of noncompact surfaces given by Ian Richards can be stated with proper rays instead of nested sequences of connected open subsets with compact boundary. I asked ...
6
votes
1
answer
370
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"Classification" of (orientable) 3-manifolds with genus-g-surface as their boundary
This is in some sense a generalization of the question I asked some time ago. I am very sorry if this question is too basic for MathOverflow, but I just started learning about some more detailed ...
- 1,429
0
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0
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140
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Can the infinite jungle gym surface be expressed by an exhaustion of compact surfaces with one boundary component?
Is it possible to write the infinite jungle gym surface as the increasing union of compact surfaces whose boundaries consist of only one simple closed curve? I believe that this is true. This surface ...
1
vote
1
answer
248
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The Schoenflies Theorem on two dimensional surfaces
Let $S$ be a surface and $U$ an open connected subset of $S$. If the frontier of $U$ in $S$ is a two sided circle $C$, then the closure of $U$ in $S$ is a surface whose boundary is $C$. I would like ...
1
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0
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225
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Is it possible to prove that surfaces with compact boundary are homeomorphic by glueing disks to the boundary components?
Let $S_1$ and $S_2$ be two surfaces with compact boundary and the same number of boundary components. Let $M_1$ and $M_2$ be the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $...
10
votes
2
answers
451
views
Group of surface homeomorphisms is locally path-connected
I think the following is true and I need a reference for the proof. (Given a closed surface $S$, i.e. a compact 2-dimensional topological manifold (without boundary), we endow $S$ with a distance ...
- 1,517
6
votes
2
answers
271
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Thrice intersecting closed geodesic on genus 2 orientable closed surface
Does there exist a closed geodesic on a closed genus 2 orientable surface (with hyperbolic metric) that self-intersects at only one point thrice?
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2
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2
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334
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A Jordan Separation Theorem for Polyhedral Surfaces
Let me begin by defining what a polyhedral surface is.
A path-connected subset $ P $ of $ \mathbb{R}^{3} $ is called a polyhedral surface iff it is the union of a finite collection $ \mathcal{C} $ of ...
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