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If the connected sum of a manifold $M$ with itself gives back $M$, does it imply $M$ is a sphere?

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#algebraic-topology #compact-manifolds
3.7k
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A non orientable closed surface cannot be embedded into $\mathbb{R}^3$

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#differential-geometry #manifolds #differential-topology #surfaces #compact-manifolds
159
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Do there exist cancellable manifolds?

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#manifolds #compact-manifolds
133
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Partition of unity. Does this one exist?

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#calculus #real-analysis #analysis #differential-geometry #compact-manifolds
223
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Compactness and Poincare duality

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#algebraic-topology #manifolds #homology-cohomology #compact-manifolds
95
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Measurability of points regular

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#ordinary-differential-equations #ergodic-theory #geometric-measure-theory #compact-manifolds
508
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Poisson equation on a Torus

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#riemann-surfaces #compact-manifolds
2.8k
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Euler characteristic of the product

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#differential-geometry #compact-manifolds
2.8k
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Degree of composition

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#differential-geometry #compact-manifolds
327
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Pullback of support of differential form

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#differential-geometry #compact-manifolds
186
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Doubts on differentiable manifolds proof: Smooth retraction of compact manifold onto its boundary

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#differential-topology #smooth-manifolds #compact-manifolds
13.2k
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Understanding Takens' Embedding theorem

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#differential-geometry #differential-topology #smooth-manifolds #chaos-theory #compact-manifolds
393
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a smooth map on a compact set can't be an immersion

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#differential-geometry #manifolds #smooth-manifolds #compact-manifolds
1.2k
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Hairy Ball Theorem: homotopy from the identity to the antipodal map

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#algebraic-topology #differential-topology #compact-manifolds
122
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if 2 compact manifolds has infinity intersection, is there any point such that the tangent space of this point are equals?

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#manifolds #smooth-manifolds #compact-manifolds #tangent-bundle

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