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    The boundary torus is not a retract of the solid torus

    P-TOP-WORKSHOP-QPH-02

    Area
    Topology
    Topics
    Fundamental Group, Retractions
    Status
    draft
    Contents

    Let \(D^2\) be the closed \(2\)-disk and \(S^1=\partial D^2\). Is \[ X=S^1\times S^1 \] a retract of \[ Y=D^2\times S^1? \] That is, does there exist a continuous map \(r:Y\to X\) whose restriction to \(X\subset Y\) is the identity?

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