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15
161
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What are the importance and power of category theory?

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#algebraic-topology #category-theory #differential-topology
156
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Transition maps/morphisms of the Hopf bundle

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#algebraic-topology #differential-topology
33
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If a composition of a nontrivial linear map with another map is smooth, is it true that the first map must be smooth?

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#differential-topology #smooth-manifolds #vector-bundles
222
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Dropping closed condition in Transversality Theorem

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#differential-topology #smooth-manifolds #submanifold #transversality
32
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The velocity filed of a curve is well defined

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#differential-geometry #differential-topology
152
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Proving this subset of $\mathbb{R}^{2}$ is not a submanifold of $\mathbb{R}^{2}$

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#differential-geometry #manifolds #differential-topology #smooth-manifolds
160
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Milnor: Morse Theory Theorem 3.1 why do we need $f^{-1}[a,b]$ to be compact?

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#differential-geometry #manifolds #differential-topology #smooth-manifolds #morse-theory
102
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Application of unexpected theorem "all closed manifolds are a quotient of $\Bbb B^n$"!

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#differential-geometry #riemannian-geometry #differential-topology #smooth-manifolds
203
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Tangent space of a sphere is locally homeomorphic to to $\mathbb{R}^{2n}$

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#differential-topology #smooth-manifolds #tangent-spaces #tangent-bundle
82
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Stiefel manifolds & number of free parameters

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#differential-geometry #manifolds #differential-topology #smooth-manifolds #stiefel-manifolds
50
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Show that a "smooth" curve intersects boundary of small enough ball at two points

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#analysis #differential-topology #curves #plane-curves
316
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What IS the Lie algebra of a Lie group?

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#lie-groups #differential-topology #lie-algebras #tangent-spaces #unitary-matrices
1.4k
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what is the universal covering of surface with genus 2

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#general-topology #algebraic-topology #differential-topology #geometric-topology #low-dimensional-topology
51
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A question about Riemannian geometry

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#geometry #differential-geometry #manifolds #riemannian-geometry #differential-topology
44
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Smoothness of function from differentiable manifold

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#derivatives #differential-topology

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