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For a Cantor set $\mathcal{C} \subset S^3$ such that $\pi_1(S^3 \setminus \mathcal{C})=0$, prove $S^3 \setminus \mathcal{C}$ can be split by a sphere.

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#general-topology #algebraic-topology #geometric-topology #low-dimensional-topology
1.2k
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Is a Möbius Strip in > 4 dimensions impossible?

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#general-topology #geometry #dimension-theory-analysis #low-dimensional-topology #dimensional-analysis
806
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Gluing the ends of a cylinder. Can we get other than a torus?

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#general-topology #algebraic-topology #low-dimensional-topology
464
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Complement of a solid genus-2-handlebody in $S^3$

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#general-topology #algebraic-topology #geometric-topology #low-dimensional-topology
1.3k
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Gluing oriented manifold along boundaries

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#general-topology #differential-geometry #algebraic-topology #manifolds #low-dimensional-topology
130
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Classification of compact 3-delta-complexes made of a single simplex

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#algebraic-topology #homology-cohomology #low-dimensional-topology
371
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Plane models from the "word"

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#geometric-topology #low-dimensional-topology
299
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Fundamental group of Antoine's necklace

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#algebraic-topology #low-dimensional-topology
55
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Calculation in From Seiberg Witten to pseudo-holomorphic curve

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#differential-geometry #symplectic-geometry #low-dimensional-topology
367
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Discontinuity of the identity function in topology

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#general-topology #analysis #geometric-topology #low-dimensional-topology
579
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Heegaard splitting and mapping class group

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#general-topology #low-dimensional-topology
322
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Lens Space Orientation Reversing Homeomorphism

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#low-dimensional-topology #compact-manifolds
115
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Reeb orbit and open books

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#low-dimensional-topology #contact-topology
78
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Surface groups as 3-manifold groups

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#low-dimensional-topology
2k
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The notion of a right-angled hexagon in hyperbolic geometry

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#hyperbolic-geometry #geometric-topology #low-dimensional-topology

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