Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57A35, 55A05

Retrieve articles in all journals with MSC: 57A35, 55A05

Additional Information

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