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How can one define parallel transport on lie groups?

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#differential-geometry #manifolds #lie-groups #lie-algebras
254
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How to find the projection of $x^2+y^2+z^2+2xyz=1$ on $S^2$?

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#differential-geometry #manifolds #vector-analysis
69
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Lie group as manifold

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#abstract-algebra #manifolds #lie-groups #smooth-manifolds
732
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Orientability of a Lie group as manifold

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#manifolds #lie-groups #smooth-manifolds #vector-fields #orientation
417
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Global frame for the cotangent bundle of a Lie group

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#differential-geometry #manifolds #lie-groups
1k
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Practical aspect of diffeomorphisms

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#differential-geometry #manifolds #smooth-manifolds
274
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How to prove the line exist?

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#differential-geometry #manifolds #differential-topology #smooth-manifolds
139
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What is the geometric object obtained by gluing together all pairs of antipodal points of an n-sphere?

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#geometry #manifolds
132
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Parallelization and existence of $N$ linearly independent vector fields

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#differential-geometry #manifolds
90
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The group $\mathrm{SU}(2)$ and the manifold $S^3$

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#group-theory #differential-geometry #manifolds
322
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Existence of canonical retraction around a compact manifold

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#geometry #differential-geometry #manifolds #differential-topology #compact-manifolds
188
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why does the tensor-product of vector-bundles exist?

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#geometry #differential-geometry #manifolds #differential-topology
337
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Curvature of $\operatorname{SL}(2)$ (manifolds)

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#differential-geometry #manifolds #lie-groups #smooth-manifolds #curvature
516
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Closed manifolds with isomorphic cohomology rings, but different cohomology modules over the Steenrod algebra

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#algebraic-topology #manifolds #examples-counterexamples #homology-cohomology #cohomology-operations
44
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Pullback of a $1$-form on $\mathbb CP^1$

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#manifolds #differential-forms

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