Talk:Solid torus

Error: I think H1 of solid torus has to be Z^2 and not Z like mentioned in the article. — Preceding unsigned comment added by tagib (talk • contribs)


 * You're mistaken: The word "solid" means this is not just the boundary, i.e. not just the 2-dimensional surface, but the interior. The fundamental group of the torus (as opposed to the fundamental group of the solid torus, is indeed Z2. But with the solid torus, if you have a path winding the short way once around the torus, you can shrink it to a point without leaving the space, since it doesn't need to stay on the boundary but can go through the interior. Michael Hardy (talk) 02:34, 30 December 2016 (UTC)

Punctuation!!


\begin{array}{rl} \textbf{right:} & H_k(S^1 \times D^2) \cong H_k(S^1) \cong \begin{cases} \mathbb{Z} & \text{if } k = 0,1, \\ 0         & \text{otherwise.} \end{cases} \\ \\ \textbf{wrong:} & H_k(S^1 \times D^2) \cong H_k(S^1) \cong \begin{cases} \mathbb{Z} & \text{if } k = 0,1 \\ 0         & \text{otherwise} \end{cases}. \end{array} $$ Notice where the period at the end of the sentence is in the "wrong" example. Apparently some people don't notice things like this. Michael Hardy (talk) 02:26, 30 December 2016 (UTC)