I have basic background in algebraic topology (Up to and including homology chapters of hatcher).
I recently saw a couple of papers that seem very interesting-
- https://arxiv.org/pdf/math/0312482.pdf
- http://www2.math.technion.ac.il/~meshulam/eprints/exp_final.pdf
- http://www2.math.technion.ac.il/~meshulam/eprints/torsion.pdf
These all seem to be giving combinatorical conditions for bounds on dimensions of homologies, I'm descrinbing this super vaugly and probably incorrectly because I haven't read the details of the proofs.
I tried searching for an introductory book but searching combinatorial topology or homology gives me classical intro books for alg. topology.
Is there a good reference?
Added as a commentor recommanded-
I am like a child asking "I know group theory, why is there no quintic formula?", and the answer I want is read about field theory (see this book), then galois theory (see this book).
My point is I feel like this is a whole well known subject and I just don't know what the name is so I can't find good surveys.