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- W2313016952 abstract "In [ 2 ], J. Gross provides an infinite collection of topologically distinct irreducible homology 3-spheres. In this paper, we construct for any finitely generated abelian group A , an infinite collection { M i } of topologically distinct irreducible closed 3-manifolds such that H 1 ( Mi ) = A for each i . The proof consists of first constructing a closed irreducible 3-manifold M A with H ( M A ) = A , and then providing a method for producing more such manifolds with the same first homology group. All maps and spaces in this paper are assumed to be in the piecewise linear category, and all subspaces are assumed to be piecewise linear subspaces. A 3-manifold M is irreducible if each 2-sphere in M bounds a 3-cell in M . A compact 2-manifold (or surface ) F in a compact 3-manifold M is properly embedded in M if F ∩ bd M = bd F ." @default.
- W2313016952 created "2016-06-24" @default.
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- W2313016952 date "1971-08-01" @default.
- W2313016952 modified "2023-10-02" @default.
- W2313016952 title "First Homology of Irreducible 3-Manifolds" @default.
- W2313016952 doi "https://doi.org/10.4153/cjm-1971-076-3" @default.
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