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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Classification of homotopy torus knot spaces
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by Richard S. Stevens
Proc. Amer. Math. Soc. 52 (1975), 461-464
DOI: https://doi.org/10.1090/S0002-9939-1975-0380807-5

Abstract:

The existence of nontrivial homotopy torus knot spaces is established as a corollary to the Theorem. Let $p$ and $q$ be two integers with $p > 1,q > 1$, and $(p,q) = 1$. Let $\mathfrak {M}$ be a maximal set of topologically distinct compact orientable irreducible $3$-mainfolds with fundamental group presented by $\langle a,b|{a^p}{b^q}\rangle$. Then card $(\mathfrak {M}) = 1/2\Phi (pq)$, where $\Phi$ denotes Euler’s function.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 461-464
  • MSC: Primary 57A35; Secondary 55A05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0380807-5
  • MathSciNet review: 0380807