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

Author: mathtuition88

http://mathtuition88.com

8 thoughts on “From Triangle to Mobius Strip”

  1. 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

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