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Proving the Stiefel Manifold is a Manifold

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#manifolds #differential-topology #smooth-manifolds
124
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How can I find a smooth map with arbitrary degree?

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#differential-geometry #manifolds #differential-topology #smooth-manifolds
75
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Is the product of a differential always equal to the differential of the product?

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#differential-geometry #differential-topology #smooth-manifolds #tangent-spaces #tangent-bundle
827
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Computing the Euler characteristic of real projective space $\mathbb{R}P^{n}$

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#algebraic-topology #differential-topology
99
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Inverse limit without category theory

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#category-theory #definition #differential-topology #limits-colimits
93
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Variational Formulation of Yamabe Problem Equivalence.

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#differential-geometry #differential-topology #curvature
244
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Local Preservation of Orientation Implies Global Preservation

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#differential-topology #smooth-manifolds
77
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Integrating over homotopy classes

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#algebraic-topology #differential-topology #homotopy-theory
159
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Let $F:\mathbb{R}^n \to \mathbb{R}^m$ be a smooth surjective submersion. Are the fibers of $F$ necessarily connected?

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#general-topology #differential-topology #fiber-bundles
52
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How can I prove $\sum\limits_{x \in f^{-1}(y)}\mkern-9mu \operatorname{sgn}(d_xf)=1$?

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#differential-geometry #differential-topology #smooth-manifolds
174
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Is the Whitney topology finer or coincide with uniform topology for codomain is $\mathbb{R}$

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#general-topology #differential-topology
103
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Degree of a smooth proper function, smooth homotopy and their pullbacks

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#differential-topology #homotopy-theory #differential-forms #pullback
71
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Tangent space of a manifold

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#manifolds #differential-topology
3.3k
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If a two variable smooth function has two global minima, will it necessarily have a third critical point?

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#real-analysis #multivariable-calculus #differential-topology #morse-theory
85
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Degree of a polynomial as smooth map - clarification

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#polynomials #differential-topology

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