1. The problem statement, all variables and given/known data I'm trying to calculate singular homology groups of the torus and Klein's bottle using the Mayer-Vietoris sequence. 3. 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 V=rectangle without the middlepoint so U is contractible thus H_n(U)=0 for n>0, H_0(U)=Z V=S1vS1 so H_1(V)=ZxZ, H_n(V)=0 and their intersection = S1, H_n(S1)=0, H_1(S1)=Z, H_0(S1)=Z Now from the M-V sequence for n>2 we get an exact sequence 0->0x0->H_n(T)->0, so H_n(T)=0. But I don't know what to do for smaller n... Please help!