Is it possible to consider $S^n$ as a $0$-simplex and a singular map of an $n$-simplex so that the $n$-simplex forms the surface of $S^n$ minus a point, and the point is the singular map of the $0$-simplex? Can a (singular map of an) $n$-simplex have zero boundary for $n>1$? I am trying to understand the homology groups of $\mathbb{R}^n$ with finitely many points removed. I imagine I could use the Mayer-Vietoris exact sequence and homotopy invariance, but I want to try to find the groups directly from the definition to confirm that I am right.
Asked
Active
Viewed 61 times
0
-
5Does this answer your question? Homology Groups of $S^n$ – John Palmieri Feb 02 '21 at 16:09
-
You have rewritten this question here. I can see that you improved the question by rewriting it. But in the future you should not create a new question to improve it: instead hit the edit button and rewrite the question. For now the best thing to do is to close this older version. – Lee Mosher Feb 02 '21 at 16:41