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Topology of indefinite orthogonal group O(p, q)

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#general-topology #algebraic-topology #manifolds #lie-groups #homotopy-theory
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Every n-manifold is a disjoint union of countably many connected n-manifolds.

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#manifolds #connectedness
1.3k
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Intuition behind "flatness" in differential geometry

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#geometry #differential-geometry #manifolds #euclidean-geometry #riemannian-geometry
17
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How to show $V$ is an open subset of $NM$?

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#manifolds #smooth-manifolds
431
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Can a manifold have zero curvature but non-zero torsion?

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#differential-geometry #manifolds #differential-forms #curvature
51
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Proving that the Grassman manifold is indeed a manifold

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#general-topology #soft-question #manifolds #differential-topology
63
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Preimage of $0$ is submanifold of $\mathbb{R}^2$

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#differential-geometry #manifolds
1.2k
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Clarifying the difference between differential 1-form and covariant derivatives

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#derivatives #differential-geometry #manifolds #differential-topology #partial-derivative
267
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definition of the hyperbolic space

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds
25
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Why do we have $dF(T_{(p,s)}W)=T_qX$?

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#manifolds #smooth-manifolds
106
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Connected sum of compact and orientable manifolds

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#general-topology #manifolds
149
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Why is this normal bundle a subset of the tangent bundle?

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#general-topology #soft-question #manifolds #differential-topology
41
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Is $dF(T_{(p,s)}W)=T_qX$ a typographical error?

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#manifolds #smooth-manifolds
76
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What minor modification author ask us to do to get $df(p)(v_p) = Df(p)(v)$?

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#calculus #manifolds #smooth-manifolds
259
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Generators of conformal isometries on two-dimensional manifolds

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#complex-analysis #differential-geometry #manifolds #mathematical-physics #conformal-geometry

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