# 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.

$\square$