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High-Dimensional Topology vs. Low-Dimensional Topology: What are the hard questions in the former?

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#geometric-topology #low-dimensional-topology
1.4k
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Does the Euler characteristic of a manifold depend upon the field of coefficients?

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#general-topology #algebraic-topology #geometric-topology
1.2k
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Is the E8 manifold homeomorphic to a CW complex?

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#manifolds #geometric-topology
60
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Notation and shorthand of cobordism G=O, SO, U

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#algebraic-topology #category-theory #geometric-topology #cobordism
2.3k
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About two notions of holonomy

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#differential-geometry #riemannian-geometry #geometric-topology #holonomy
92
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Why is this a group action?

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#group-theory #algebraic-topology #group-actions #geometric-topology
349
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Number of connected components of this complement

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#general-topology #algebraic-topology #connectedness #geometric-topology
935
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About generalized Schoenflies problem in the smooth category

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#geometric-topology
94
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Homeomorphisms of product spaces: an example

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#examples-counterexamples #geometric-topology
338
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Surgery results in a cylinder

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#general-topology #differential-topology #geometric-topology #low-dimensional-topology #surgery-theory
416
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Closed 4-manifolds with uncountably many differentiable structures

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#examples-counterexamples #geometric-topology #low-dimensional-topology
98
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Why are homotopy spheres spin-cobordant in dimensions divisible by 4?

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#algebraic-topology #manifolds #geometric-topology #cobordism
128
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Questions about the Nature of Chirality (with some focus on dimensionality)

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#general-topology #geometric-topology #dimension-theory-analysis #low-dimensional-topology
148
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Extensions of diffeomorphisms of $S^2$ and the connectedness of $\text{Diff}^+(S^2)$

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#differential-topology #geometric-topology
1.1k
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What is a manifold with cusp?

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#manifolds #hyperbolic-geometry #geometric-topology

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