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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Inclusion maps of $3$-manifolds which induce monomorphisms of fundamental groups
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by Jože Vrabec PDF
Trans. Amer. Math. Soc. 214 (1975), 75-93 Request permission

Abstract:

The main result is the following “duality” theorem. Let M be a 3-manifold, P a compact and connected polyhedral 3-submanifold of $\int M$, and X a compact and connected polyhedron in $\int P$. If ${\pi _1}(X) \to {\pi _1}(P)$ is onto, then ${\pi _1}(M - P) \to {\pi _1}(M - X)$ is one-to-one. Some related results are proved, for instance: we can allow P to be noncompact if also X satisfies a certain noncompactness condition: if M lies in a 3-manifold W with ${H_1}(W) = 0$, then the condition that ${\pi _1}(X) \to {\pi _1}(P)$ is onto can be replaced by the weaker one that ${H_1}(X) \to {H_1}(P)$ is onto.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 214 (1975), 75-93
  • MSC: Primary 57A10
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0388398-4
  • MathSciNet review: 0388398