From Triangle to Mobius Strip

What familiar space is the quotient \Delta-complex of a 2-simplex [v_0,v_1,v_2] obtained by identifying the edges [v_0,v_1] and [v_1,v_2], preserving the ordering of vertices?

This is a question from Hatcher. So if we “glue” two edges of the triangle together, preserving order, we get a Mobius Strip!

triangle1

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8 Responses to From Triangle to Mobius Strip

  1. nkpithwa says:

    Thanks for this simple, yet inspirational example from Hatcher. It reminds that Prof. Allen Hatcher’s Notes on Topology are available somewhere from web. (I had downloaded them long back). BTW, it inspires me to put some stuff on mobius strip for fun in my own blog ! 🙂

    Liked by 1 person

  2. When you say “glue” two edges together we can make an Möbius strip, can further explain your discovery with an example?

    Liked by 1 person

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