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Is there a more formal way to prove Liouville's theorem on the conservation of symplectic volume?

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#differential-geometry #manifolds #symplectic-geometry #hamilton-equations
362
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The motivation of differential forms

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#integration #differential-geometry #manifolds #differential-topology
107
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$S^2$ as $3$-manifold with boundary

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#general-topology #manifolds #spheres
55
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What does $P\times_G V\to B$ mean?

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#general-topology #differential-geometry #manifolds #vector-bundles #principal-bundles
355
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Integrating a density over a Mobius strip

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#integration #manifolds #differential-forms #mobius-band
66
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Flows on manifolds

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#analysis #geometry #differential-geometry #manifolds
363
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Integral over "infinitesimal" transformed manifold

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#integration #manifolds #smooth-manifolds #stokes-theorem
874
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Fundamental group of a manifold minus a submanifold

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#general-topology #algebraic-topology #manifolds #fundamental-groups
267
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Glueing manifolds with boundaries and Seifert-Van Kampen theorem

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#general-topology #algebraic-topology #manifolds #fundamental-groups
206
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Is every open subset of a manifold homeomorphic to some Euclidean space?

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#general-topology #manifolds #differential-topology
97
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Manifolds, where its enough to have one chart for integration

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#integration #differential-geometry #manifolds #riemannian-geometry #volume
290
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Reducible Heegaard splittings can be written as connected sums

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#general-topology #manifolds #geometric-topology #low-dimensional-topology
32
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Show that $\mathcal D_p(M)=\text{span}\left(\left.\frac{\partial }{\partial x^1}\right|_p,...,\left.\frac{\partial }{\partial x^n}\right|_p\right)$

Published on
#manifolds
978
Views

Smooth manifold which is a group, but not a Lie Group

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#differential-geometry #manifolds #differential-topology #lie-groups #smooth-manifolds
6.4k
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Show that a submersion is open

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#manifolds #smooth-manifolds

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