Search the corpus

    Identify a mapping cylinder and a mapping torus

    P-UNL871F13-PS10.1

    Area
    Topology
    Topics
    Homotopy, Quotient Spaces
    Status
    draft
    Contents

    Identify a familiar space homeomorphic to each of the following constructions, and prove your answer geometrically.

    1. The mapping cylinder of \[ f:I\to S^1,\qquad f(t)=(\cos(4\pi t),\sin(4\pi t)). \]

    2. The mapping torus of \[ f:S^1\to S^1,\qquad f(x,y)=(x,-y). \]

    Solution submission

    Submit a solution on GitHub

    Source Collections