Recent content by ddo

\mathbb{Z}\times\mathbb{Z} \rightarrow\mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z} The kernel of the right map is 0, so the image of the left map is 0, so the kernel of the left map is \mathbb{Z}\times\mathbb{Z} Next: \mathbb{Z}\times\mathbb{Z}\rightarrow...

Thank for your reply! I suppose the Mayer-Vietoris hint was there to make the task easier :) So H_0 is Z because there is only one connected component, H_1 is the abelianization of the fundamental group, both torus and Klein's bottle have abelian fundamental groups so for torus it's Z \times...

Homework Statement I'm trying to calculate singular homology groups of the torus and Klein's bottle using the Mayer-Vietoris sequence. The Attempt at a Solution I represent both spaces as a rectangle with identified edges. Then I take the sets: U=rectangle without the boundary...