Cloverleaf representations of simply connected $3$-manifolds
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- by Edwin E. Moise PDF
- Trans. Amer. Math. Soc. 201 (1975), 1-30 Request permission
Abstract:
Let $M$ be a triangulated $3$-manifold satisfying the hypothesis of the Poincaré Conjecture. In the present paper it is shown that there is a finite linear graph ${K_1}$ in the $3$-sphere, with exactly two components, and a finite linear graph ${K_2}$ in $M$, such that when the components of the graphs ${K_i}$ are regarded as points, the resulting hyperspaces are homeomorphic. ${K_2}$ satisfies certain conditions which imply that each component of ${K_2}$ is contractible in $M$. Thus the conclusion of the theorem proved here is equivalent to the hypothesis of the Poincaré Conjecture.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 201 (1975), 1-30
- MSC: Primary 57C05; Secondary 57A10, 57C40
- DOI: https://doi.org/10.1090/S0002-9947-1975-0350745-7
- MathSciNet review: 0350745