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Existence of pullback tensor

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#differential-geometry #manifolds
703
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Wedge product: $\,\omega \wedge \eta= (-1)^{kl} \eta \wedge \omega$

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#linear-algebra #differential-geometry #manifolds #differential-forms #exterior-algebra
309
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Given a smooth map, find another similar map with a differential that is never zero (Guillemin and Pollack 2.3.8).

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#manifolds #differential-topology
215
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Clarifying a point in Guillemin and Pollack on a certain submersion

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#manifolds #differential-topology
244
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Why is it impossible for a compact connected non-orientable $n$-manifold to be the suspension of some connected based space?

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#manifolds #compact-manifolds
3.6k
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Manifold and maximal atlas

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#manifolds
316
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Using Mayer-Vietoris to show $\chi(M) = \chi(U)+\chi(V)-\chi(U \cap V)$

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#manifolds #homology-cohomology
1.9k
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A product of smooth manifolds together with one smooth manifold with boundary is a smooth manifold with boundary

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#general-topology #differential-geometry #manifolds #differential-topology #smooth-manifolds
352
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Non-diffeomorphic structures on the sphere

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#manifolds #differential-topology #geometric-topology
255
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Riemannian manifolds isometry

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#differential-geometry #manifolds #riemannian-geometry
2.3k
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What's the cohomology of disjoint union of two circles

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#algebraic-topology #manifolds #differential-topology
375
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Rigorous Definition On composition of Multivariable Functions

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#calculus #real-analysis #multivariable-calculus #derivatives #manifolds
1.5k
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Lie derivative of the product of a function and a form

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#differential-geometry #manifolds #lie-derivative
88
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Clarification about differentiable manifolds

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#manifolds #differential-topology
818
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Divergence, contraction and lie derivatives

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#manifolds #differential-forms #lie-derivative

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