Spheres and homology groups

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April 14th 2012, 08:15 AM
kierkegaard

Spheres and homology groups

Prove that $S^{m+n+1}=X\cup Y$ with $X\cong S^{m}\times B^{n+1}$ , $Y\cong B^{m+1}\times S^{n}$ , and $X\cap Y\cong S^{m} \times S^{n}$ . Use this to compute the homology groups of $S^m \times S^n$ .

Thanks.

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