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Is the Hopf fibration the only fibration with total space $S^{3}$?

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#algebraic-topology #differential-topology #fiber-bundles #hopf-fibration
215
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How do we understand and visualize the meridians of a 3-sphere?

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#general-topology #manifolds #euclidean-geometry #stereographic-projections #hopf-fibration
1.6k
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Metric on total space, connection and Hopf fibration

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#metric-spaces #fiber-bundles #connections #hopf-fibration
162
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Lie Bracket, Hopf Fibration, independence of choice

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#differential-geometry #hopf-fibration
785
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The rotation group $SO(3)$ may be mapped to a $2$-sphere by sending a rotation matrix to its first column. How can I describe the fibres of the map?

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#linear-algebra #abstract-algebra #rotations #linear-groups #hopf-fibration
371
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fibration of complex projective space over quaternion projective space

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#geometry #algebraic-topology #differential-topology #fibration #hopf-fibration
484
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Using Hopf fibration to calculate $\pi_{3} (S^2)$

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#algebraic-topology #proof-writing #fundamental-groups #fibration #hopf-fibration
822
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How does the Hopf map generate $\pi_3(S^2)$?

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#general-topology #algebraic-topology #hopf-fibration #higher-homotopy-groups
248
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Simple Characterization of the Hopf Fiberation as Cosets of the Circle Group (Stabilizer of a Point)

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#abstract-algebra #lie-groups #rotations #quaternions #hopf-fibration
530
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Proving Linkedness of Hopf Fibers

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#differential-geometry #algebraic-topology #manifolds #quaternions #hopf-fibration
349
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Hopf submersion

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#differential-geometry #differential-topology #smooth-manifolds #hopf-fibration
710
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Why is the curvature of the connection $\bar{z_1}dz_1 + \bar{z_2}dz_2$ on the Hopf fibration not exact?

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#differential-geometry #principal-bundles #hopf-fibration
81
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Seeing $\mathbb{S}^3$ as a pullback

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#algebraic-topology #manifolds #smooth-manifolds #characteristic-classes #hopf-fibration
119
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What does the surface |z₁|² = |z₂|² look like?

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#complex-geometry #surfaces #quaternions #spheres #hopf-fibration
251
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How to get latitudinal tori using the inverse Hopf map?

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#algebraic-topology #inverse-function #hopf-fibration

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