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15
58
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Is there an intuitive way to see why $\mathbb{P}^2$ is non-orientable?

Published on
#smooth-manifolds #non-orientable-surfaces
117
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The pushforward of transition function of an orientable Riemannian manifold is in $SO(n)$?

Published on
#riemannian-geometry #smooth-manifolds #pushforward
818
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Smooth covering maps and the fundamental group

Published on
#differential-geometry #smooth-manifolds #covering-spaces #automorphism-group
35
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Calculate the integral over a surface.

Published on
#vector-analysis #smooth-manifolds
363
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Left translation on Lie group of a discrete subgroup is properly discontinuous

Published on
#differential-geometry #algebraic-topology #differential-topology #lie-groups #smooth-manifolds
262
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Topological invariance of compactly supported de Rham cohomology

Published on
#differential-geometry #differential-topology #smooth-manifolds #differential-forms #de-rham-cohomology
524
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Determining the linear independence of tangent vectors at a point on the manifold

Published on
#differential-topology #smooth-manifolds #tangent-bundle #smooth-functions #tangent-spaces
57
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Stiefel-Whitney numbers of exotic differentiable structures

Published on
#differential-topology #smooth-manifolds #characteristic-classes
536
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Stiefel-Whitney numbers of manifolds that are boundaries of non-smoothable manifolds

Published on
#differential-topology #smooth-manifolds #characteristic-classes #cobordism
44
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Question related to orientation on a arbitrary oriented manifold

Published on
#differential-geometry #manifolds #smooth-manifolds #differential-forms #orientation
97
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Are real linear maps of smooth sections locally determined?

Published on
#differential-geometry #manifolds #differential-topology #smooth-manifolds #vector-bundles
62
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The existence of a smooth vector field locally

Published on
#differential-geometry #smooth-manifolds #vector-fields
87
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Please explain the repeated gradient of a function on manifold.

Published on
#geometry #differential-geometry #manifolds #riemannian-geometry #smooth-manifolds
331
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Are algebraic groups defined over $\mathbb{R}$ Lie groups?

Published on
#algebraic-geometry #lie-groups #smooth-manifolds #algebraic-groups
68
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$(0,3)$ as a non-Hausdorff smooth manifold

Published on
#general-topology #manifolds #smooth-manifolds

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