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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0380807-5
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 $\langle a,b|{a^p}{b^q}\rangle$. Then card $(\mathfrak {M}) = 1/2\Phi (pq)$, where $\Phi$ denotes Euler’s function.


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Keywords: Compact orientable <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img5.gif" ALT="$3$">-mainfold, lens space, Seifert fiber space, spine, <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$2$">-complex corresponding to group presentation
Article copyright: © Copyright 1975 American Mathematical Society