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7 votes
4 answers
996 views

Amending flawed "proof" that homology groups are zero

I am trying to prove a certain statement that seems true based on computational data, and there is a nice argument that proves it, assuming all cycles are the simplest ones (e.g., when the only 1-cycl …
Marcel K. Goh's user avatar
3 votes
0 answers
130 views

Homology groups of a certain simplicial complex

I've run across a simplicial complex which, according to Sage, seems to have a very easily-described homology. However, proving this fact has been rather difficult. Fix $s\ge 2$ (though I would be ver …
Marcel K. Goh's user avatar
1 vote

Amending flawed "proof" that homology groups are zero

Following Andy Putman's suggestion that we use the nerve complex, I believe I have found an inductive proof that $H_1(X_n) = 0$ for all $n$. Please point out errors if you see any! Let $X_n$ denote th …
Marcel K. Goh's user avatar