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Groups $\pi$ with $K(\pi, 1)$ a finite CW-complex

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#algebraic-topology #manifolds #open-problem
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Normal coordinates and the metric tensor

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#real-analysis #analysis #differential-geometry #manifolds #riemannian-geometry
432
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Jacobi field along every geodesic?

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#real-analysis #analysis #differential-geometry #manifolds #riemannian-geometry
166
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Compute the volume element in a differentiable manifold.

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#analysis #multivariable-calculus #manifolds
1.1k
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Can (singular) homology classes always be represented by images of closed manifolds?

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#algebraic-topology #manifolds #homology-cohomology
346
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Homeomorphism in the definition of a manifold

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#manifolds #differential-topology
185
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Can a $1d$ space never be curved?

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#real-analysis #differential-geometry #manifolds #differential-topology #riemannian-geometry
169
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Angle form, 1-form, proof verification.

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#real-analysis #general-topology #multivariable-calculus #differential-geometry #manifolds
96
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Does map induced by rotation preserve the volume form?

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#real-analysis #general-topology #multivariable-calculus #differential-geometry #manifolds
549
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The integral of a closed form along a closed curve is proportional to its winding number

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#general-topology #multivariable-calculus #differential-geometry #manifolds #differential-topology
1.6k
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The definition of a differentiable vector field on a manifold

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#real-analysis #manifolds #smooth-manifolds
294
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Representation of sum of homology classes

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#algebraic-topology #manifolds #homology-cohomology
135
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Zips and Zippers

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#general-topology #manifolds #differential-topology #smooth-manifolds
163
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Normal coordinates

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#real-analysis #differential-geometry #manifolds #riemannian-geometry
366
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Is a polyhedron an affline manifold?

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#differential-geometry #algebraic-topology #manifolds #linear-programming

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