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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the torus theorem and its applications


Author: C. D. Feustel
Journal: Trans. Amer. Math. Soc. 217 (1976), 1-43
MSC: Primary 57A10
DOI: https://doi.org/10.1090/S0002-9947-1976-0394666-3
MathSciNet review: 0394666
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Abstract: In this paper, we prove the torus theorem and that manifolds in a certain class of 3-manifolds with toral boundary are determined by their fundamental groups alone. Both of these results were reported by F. Waldhausen. We also give an extension of Waldhausen's generalization of the loop theorem.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0394666-3
Keywords: Torus, annulus, essential map, essential embedding
Article copyright: © Copyright 1976 American Mathematical Society