Rudy the Reindeer
Reputation
21,610
77/100 score
 Aug 14 comment Homology of Euclidean space $H_n(\mathbb{R}^m)$ @gary: thanks anyway, for trying! Aug 14 revised Homology of Euclidean space $H_n(\mathbb{R}^m)$ added 79 characters in body Aug 13 answered Homology of Euclidean space $H_n(\mathbb{R}^m)$ Aug 13 revised Homology of Euclidean space $H_n(\mathbb{R}^m)$ added 115 characters in body Aug 13 accepted Question about deformation retracts and neighbourhoods Aug 13 asked Homology of Euclidean space $H_n(\mathbb{R}^m)$ Aug 11 awarded Tumbleweed Aug 11 accepted False proof of $H_0 ( X) = 0$ Aug 10 comment False proof of $H_0 ( X) = 0$ Ok, Chris maybe you can make your comment into an answer so that I can accept it. Many thanks for your help! Aug 10 comment False proof of $H_0 ( X) = 0$ Oh!! $\{ c\}$, $\{c + c\}$, $\dots$ are all different elements of $H_0 (X)$. That's what you're saying? Aug 10 comment False proof of $H_0 ( X) = 0$ Because it's a group and it only has one element, so that element has got to be neutral element otherwise it's not a group. Aug 10 asked False proof of $H_0 ( X) = 0$ Aug 10 comment Question about the sum of chain groups Yes I do : ) (some more characters) Aug 10 comment Question about the sum of chain groups No! I think I finally got it: for the boundary map $\partial: C(X) = C (A \cup B) \rightarrow C(X)$ it holds that $\partial ( C ( A + B) ) \subset C( A + B)$. And the reason why is because $C(A)$ and $C(B)$ are chain complexes. Aug 10 comment Question about the sum of chain groups Actually no, I think you meant to write "...Since the boundary map of $C(A + B)$ restricts to $C(A + B)$ (why?),..."! Aug 10 comment Question about the sum of chain groups I think you meant to write "...Since the boundary map of $C(A \cup B)$ restricts to $C(A \cup B)$ (why?),...", because e.g. $\sigma$ in the picture is a simplex in $C(A\cup B)$ with 2 of its 3 boundaries in $C(A \cup B) - C(A + B)$. Aug 10 comment Question about the sum of chain groups GeoGebra looks really good, I had never heard of it before. I do all my drawing on paper, how old fashioned : D Aug 9 comment Computing $H_1(X)$ using Hurewicz Hey, thanks! I think I'm using Hurewicz theorem, maybe it's called Poincare for $n=1$ : ) Aug 9 comment Question about the sum of chain groups I wish I could give you more up votes for all this effort you put into writing this answer. Aug 9 comment Question about the sum of chain groups Actually, I do draw pictures. I've been following your advice on more than one occasion... and I appreciate your help! I think I should chuck Hatcher, every now and again there is a passage in it that is utterly unhelpful : (