Ah, we haven't done homology yet
If I considered the torus as the quotient of a square in the usual way (opposite sides identified with the same orientations), and puncture a hole in it, then can I (forgoing any sort of use of actual terminology) expand the hole so that I only have the boundary of the square left? And then identifying the edges I get the wedge of two circles?
Does that sound more...usual?
And then, would a simple circle be the deformation retraction of the torus?
But then, if I had a surface of genus g,
I could represent that as the connected sum of g tori...but then I don't know how to go about using the above approach to determine what it retracts to.
I mean, if I removed one point, I must still have the figure of 8 graph in there somewhere, but what do I do with the other
tori that don't have a hole removed?
Sorry if this is all total garbage again - I haven't quite got my head around it yet
"It's never crowded along the extra mile"
Graduated, and done with maths forever