/sci/ - Science & Math

>>11168720
No, not really. That's more like homotopy.
You have a surface. You take out your pen, and you draw a triangle in it (sides need not be straight lines). If you can use your pen to paint the "inside" of the triangle, there isn't a hole there. If you can't, then there is one. Of course, on a sphere or in some other surfaces, the choice of inside is arbitrary, but you can still choose one and fill it in.
You might think that in something like a torus there will be just too many triangles that can't be filled in, but we also consider two different triangles drawn in a surface to be "homologous" if we can consider them as a double boundary and fill in the area between them.
Of course, there's only so much of the intuition that can be explained without knowledge of the formalism. I personally recommend Fuchs-Fomenko.