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"Using a ## \Delta ## complex, compute the homology groups of the quotient space obtained fromt the 2-sphere ##S^2## by identifying three of its distinct points."

Similarly I have a question about a torus with two points identified.

I have a pretty good idea of how to compute homology groups with a ## \Delta ## complexes now for the Torus, Projective Plane, Klein bottle, etc. But what I am not understanding is what happens when I identify points to one another. i.e. I generally have some polygonal region ##I \times I## divided into triangles, i.e. for the Klein bottle:

But I don't know what happens to t his structure when I pick some points on them and start identifying them. What does my complex look like?

-Dave K