Geodesic
First Homology of Irreducible 3-Manifolds
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 686-691

Voir la notice de l'article provenant de la source Cambridge University Press

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 {Mi } 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 MA with H(MA ) = 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 ∩ bdM = bdF. 
Evans, Benny. First Homology of Irreducible 3-Manifolds. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 686-691. doi: 10.4153/CJM-1971-076-3
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