Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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\vert{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

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0380807-5
PII: S 0002-9939(1975)0380807-5
Keywords: Compact orientable $ 3$-mainfold, lens space, Seifert fiber space, spine, $ 2$-complex corresponding to group presentation
Article copyright: © Copyright 1975 American Mathematical Society