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Compact 1-manifolds

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#general-topology #algebraic-topology #manifolds #geometric-topology #compact-manifolds
67
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How does one compute the Hurewicz homomorphism for a (symplectic) nilmanifold?

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#lie-algebras #homology-cohomology #homotopy-theory #symplectic-geometry #compact-manifolds
62
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Are there any nontrivial second Hurewicz homomorphisms for familiar compact 6-dimensional manifolds?

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#algebraic-topology #homology-cohomology #homotopy-theory #group-homomorphism #compact-manifolds
104
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Is there a preferred way to characterize a cone in cohomology?

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#algebraic-geometry #differential-geometry #homology-cohomology #smooth-manifolds #compact-manifolds
394
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line sub-bundles over an $ n $ -sphere.

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#differential-geometry #vector-bundles #compact-manifolds
651
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Total Gaussian curvature

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#differential-geometry #surfaces #curvature #compact-manifolds
80
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Prove or disprove: for every nonzero $\phi \in H^k(M),$ there is $\psi \in H^{n-k}(M)$ with $\phi \cup \psi \neq 0$

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#algebraic-topology #homology-cohomology #compact-manifolds
277
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How can I show $R^n$ is dense in $S^n$?

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#general-topology #compactness #compact-manifolds
201
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Is the hemisphere of $S^4$ the unique compact 4-dimensional manifold with $\partial K = S^3$?

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#differential-geometry #algebraic-topology #compact-manifolds #manifolds-with-boundary #orbifolds
73
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Coverings of a three-manifold

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#algebraic-topology #manifolds #covering-spaces #compact-manifolds
57
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Why are PDEs with Hamiltonians usually solved on compact manifolds?

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#partial-differential-equations #manifolds #regularity-theory-of-pdes #compact-manifolds #hamilton-jacobi-equation
1.7k
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connected sum of surfaces is well defined proof attempt

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#general-topology #algebraic-topology #manifolds #compact-manifolds
329
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A lemma in Milnor's book "Topology from the Differentiable Viewpoint"

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#differential-topology #implicit-function-theorem #compact-manifolds
881
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Proper map and manifolds

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#general-topology #differential-geometry #differential-topology #compact-manifolds
233
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Surjectivity of the exponential map on SO(2n)/U(n)

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#differential-geometry #manifolds #compact-manifolds #homogeneous-spaces

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