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Proceedings of the American Mathematical Society

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



Classification of homotopy torus knot spaces

Author: Richard S. Stevens
Journal: Proc. Amer. Math. Soc. 52 (1975), 461-464
MSC: Primary 57A35; Secondary 55A05
MathSciNet review: 0380807
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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\vert{a^p}{b^q}\rangle $. Then card $ (\mathfrak{M}) = 1/2\Phi (pq)$, where $ \Phi $ denotes Euler's function.

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Keywords: Compact orientable $ 3$-mainfold, lens space, Seifert fiber space, spine, $ 2$-complex corresponding to group presentation
Article copyright: © Copyright 1975 American Mathematical Society