File:Homotopy lifting gif.gif

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    Summary

    Description
    English: Homotopy of a loop f:[0,1]→𝕋2 (the grey curve) on the torus and a lift of the same homotopy to the covering space ℝ2. The plane curve is the lift f~ of f to this covering space.
    Date
    Source Own work
    Author Emgram

    Made using desmos.com/3d with the beta3d search parameter and the DesModder Chrome extensive

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    I, the copyright holder of this work, hereby publish it under the following license:
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    Captions

    A torus with a curve on the surface which animates in time. Below, a the curve appears lifted to the covering space R^2

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    depicts

    2 February 2026

    3,004,858 byte

    900 pixel

    900 pixel

    image/gif

    834f821bcce3124d286789996d333054a8096f61

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    Date/TimeThumbnailDimensionsUserComment
    current18:57, 3 February 2026Thumbnail for version as of 18:57, 3 February 2026900 × 900 (2.87 MB)wikimediacommons>Emgramcorrected mathematics

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