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## Fundamenta Mathematicae

2003 | 177 | 3 | 193-208
Tytuł artykułu

### On the structure of closed 3-manifolds

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
We will show that for every irreducible closed 3-manifold M, other than the real projective space P³, there exists a piecewise linear map f: S → M where S is a non-orientable closed 2-manifold of Euler characteristic χ ≡ 2 (mod 3) such that $|f^{-1}(x)| ≤ 2$ for all x ∈ M, the closure of the set ${x ∈ M : |f^{-1}(x)| = 2}$ is a cubic graph G such that $S - f^{-1}(G)$ consists of 1/3(2-χ) + 2 simply connected regions, M - f(S) consists of two disjoint open 3-cells such that f(S) is the boundary of each of them, and f has some additional interesting properties. The pair $(S,f^{-1}(G))$ fully determines M, and the minimal value of 1/3(2-χ) is a natural topological invariant of M. Given S there are only finitely many M's for which there exists a map f: S → M with all those properties. Several open problems concerning the relationship between G and M are raised.
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Tom
Numer
Strony
193-208
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
• Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, U.S.A.
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