Hatcher 2.1.2

Hatcher, Algebraic Topology, Chapter 2, Section 1

2. Show that the \Delta-complex obtained from \Delta^3 by performing the edge identifications [v_0,v_1]\sim[v_1,v_3] and [v_0,v_2]\sim[v_2,v_3] deformation retracts to a Klein bottle. Find other identifications of edges that produce \Delta-complexes deformation retracting onto a torus, a 2-sphere, and \mathbb{R}P^2.
Proof.

\square

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