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Getting acquainted with preimage orientation

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#general-topology #manifolds #differential-topology #smooth-manifolds
355
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How to find basis of a de Rham Cohomology group?

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#general-topology #geometry #differential-geometry #differential-topology #smooth-manifolds
199
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Darboux theorem and symplectic 2-sphere

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#smooth-manifolds #curvature #symplectic-geometry
434
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Focal points in abstract sense

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#differential-geometry #manifolds #differential-topology #smooth-manifolds
257
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Finding an explicit smooth atlas for $GL_n(\mathbb{R})$

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#differential-geometry #manifolds #smooth-manifolds
147
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Why are data points which are “close” should have a “similar” label?

Published on
#matrices #graph-theory #manifolds #smooth-manifolds
293
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Is every compact solvmanifold the quotient of a simply connected solvable Lie group by a discrete subgroup?

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#differential-geometry #lie-groups #smooth-manifolds #solvable-groups
1.5k
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About the construction of the restriction of a Vector Bundle in John M. Lee's book

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#smooth-manifolds #vector-bundles
80
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How to prove $\frac{\partial}{\partial x^r} (x^r) = 1$ where $(U, (x^1, ..., x^n))$ is a local chart of a smooth manifold.

Published on
#differential-geometry #smooth-manifolds #intuition
303
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Manifold parallelizable equivalent condition

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#differential-geometry #manifolds #smooth-manifolds
216
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Why are $(q,p)$ in cotangent bundle instead of tangent bundle?

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#smooth-manifolds #classical-mechanics #tangent-bundle #co-tangent-space
740
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Derivative of a tangent bundle projection

Published on
#geometry #differential-geometry #manifolds #smooth-manifolds
282
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Existence of an embedding of a smooth manifold?

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#differential-topology #smooth-manifolds
464
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Can an injective smooth map from a smooth manifold into another smooth manifold have a discontinuous inverse?

Published on
#differential-geometry #manifolds #smooth-manifolds
522
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Question of deck transformation on double cover $\tilde{M}$ of non-orientable manifold $M$.

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#general-topology #riemannian-geometry #smooth-manifolds #geometric-topology #orientation

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