Mention simplicial homology for math newbies?

[simnalamburt]

What do you think about introducing homology by first explaining simplicial homology before moving on to singular homology? It feels like it could give readers a more intuitive grasp of what homology is. Since you are the author of this book, I’d really like to hear your thoughts.

If you agree with the idea but don’t have time to make the edits yourself, I’d be happy to try drafting a version. (I don’t have a fully concrete proposal yet though)

[user202729]

not the author, but I sort of agree. (okay not really, I think singular homology is actually more intuitive than simplicial homology except that you cannot easily compute it — I mean, it's pretty obvious that there is no 2-cell in the torus whose boundary is a non-nulhomotopic loop, but how do you prove it?)

[vEnhance]

Currently there is a chapter later on cellular homology, which IIRC does most of what simplicial homology does anyway (by being easier to compute but harder to prove things about) --- I think in practice people tend to use CW rather than simplicial (?). I don't know if it might be redundant to have both that bonus chapter and then another one on simplicial homology? Open to being persuaded.

[simnalamburt]

I’ll put this issue on hold for now. After studying homology for a few more months, I’ll come back with a more precise proposal.