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Corollary 41.3:

Suppose $ A$ is a subset of $ S^n$ homeomorphic to $ S^k$ for some $ k$, $ 0\leq k \leq n-1$, then

$\displaystyle H_j(S^n - A) = \left\{\begin{array}{lll} \mathbb{Z}\oplus\mathbb{... ...- k - 1 \neq 0 \\ 0 & & \mbox{otherwise}. \\ \end{array} \right.\eqno(41.5) $


nisha 2012-03-20