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15
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$Y \times [0, 1)$ is locally Euclidean

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#general-topology #algebraic-topology #manifolds
53
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Rank of a Poisson structure is always even

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#manifolds #poisson-geometry
79
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Rank of Poisson matrix and rank of Poisson structure are equal

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#manifolds #poisson-geometry
69
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Tangent space at a point in invertible upper triangular matrices

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#differential-geometry #manifolds #lie-groups #smooth-manifolds #tangent-spaces
149
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Any closed orientable $3$-manifold admits a Heegaard splitting

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#manifolds #geometric-topology #low-dimensional-topology
126
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Stabilization of Heegaard splitting

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#manifolds #geometric-topology #low-dimensional-topology
51
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Hyperplanes question in Tu's book on Manifolds

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#vector-spaces #manifolds #exterior-algebra #direct-sum
124
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Why is $X(\varphi^*f)=(\varphi_*X)f$?

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#differential-geometry #manifolds
357
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Another definition of a smooth map between manifolds

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#solution-verification #manifolds #smooth-manifolds #smooth-functions
65
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How to find a function $f: \mathbb{R}^2\to \mathbb{R}$ to show that $a = df$.

Published on
#analysis #manifolds
134
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Find the volume of $\mathbb S^n$ (the surface area of $(n+1)$-dimensional unit ball) by using differential geometry

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#differential-geometry #manifolds #smooth-manifolds #differential-forms #volume
60
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Question regarding submanifolds of submanifolds

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#real-analysis #differential-geometry #manifolds #differential-topology
46
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How to find the isomorphism between Lie algebra $L_{0}$ and $L_{1}$?

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#manifolds #lie-groups #lie-algebras #vector-fields #vector-space-isomorphism
48
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Proof of the fact that $\mathfrak{g}\otimes C^{\infty}(S^1) \cong C^{\infty}(S^1;\mathfrak{g})$

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#manifolds #lie-algebras #tensor-products #complex-manifolds
30
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How does one decompose a closed set into polyhedral k-chains or chainlets? Is there a decomposition or approximation theorem available?

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#geometry #measure-theory #manifolds #approximation-theory

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