In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} . That is, H 0 ( X , Z ) = H n ( X , Z ) = Z {\displaystyle H_{0}(X,\mathbb {Z} )=H_{n}(X,\mathbb {Z} )=\mathbb {Z} } and H i ( X , Z ) = { 0 } {\displaystyle H_{i}(X,\mathbb {Z} )=\{0\}} for all other i.
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} . That is, H 0 ( X , Z ) = H n ( X , Z ) = Z {\displaystyle H_{0}(X,\mathbb {Z} )=H_{n}(X,\mathbb {Z} )=\mathbb {Z} } and H i ( X , Z ) = { 0 } {\displaystyle H_{i}(X,\mathbb {Z} )=\{0\}} for all other i.
Source: Wikipedia "Homology sphere" · CC BY-SA 4.0
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