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15
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Sufficient condition for $\mathbb{Z}$-orientability

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#algebraic-topology #manifolds #orientation
902
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If $M$ is a 4-dimensional, compact, simply connected manifold with boundary, what is the topology of $\partial M$?

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#algebraic-topology #manifolds #homology-cohomology #geometric-topology
546
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Topological properties of regular and critical points and values

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#real-analysis #differential-geometry #manifolds #differential-topology
355
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Can someone illustrate the definition of manifold with a simple example?

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#differential-geometry #manifolds #differential-topology #smooth-manifolds
120
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Integral Over the N-Sphere in the framework of chains:

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#integration #differential-geometry #manifolds #differential-forms #geometric-topology
45
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Connection and curve

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#real-analysis #differential-geometry #manifolds #riemannian-geometry #curvature
119
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Cartan geometry on manifolds with boundary

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#differential-geometry #manifolds #principal-bundles #manifolds-with-boundary #cartan-geometry
51
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How can we show that $S^0$ is a manifold?

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#differential-geometry #manifolds
1k
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The closure of an open set in $\mathbb{R}^n$ is a manifold

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#analysis #manifolds
90
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Manifold notes in more informal way

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#manifolds
84
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Try to use Homogeous space Characterize the space of all lines in the plane .

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#differential-geometry #manifolds #smooth-manifolds #homogeneous-spaces
1.3k
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Confused with The Transversality Theorem when all manifolds are boundaryless

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#differential-geometry #manifolds #differential-topology #smooth-manifolds #geometric-topology
258
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How do ideas in differential geometry expand upon ideas from introductory calculus

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#calculus #multivariable-calculus #differential-geometry #manifolds #vector-fields
621
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Fundamental class of the connected sum of two closed orientable manifolds

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#algebraic-topology #manifolds #homology-cohomology #orientation
405
Views

Revolving a $k$-manifold around an axis gives a $(k+1)$-manifold

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#analysis #differential-geometry #manifolds #smooth-manifolds

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