Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Cyclic actions on lens spaces
HTML articles powered by AMS MathViewer

by Paik Kee Kim PDF
Trans. Amer. Math. Soc. 237 (1978), 121-144 Request permission

Abstract:

A 3-dimensional lens space $L = L(p,q)$ is called symmetric if ${q^2} \equiv \pm 1 \bmod p$. Let h be an orientation-preserving PL homeomorphism of even period $n( > 2)$ on L with nonempty fixed-point set. We show: (1) If n and p are relatively prime, up to weak equivalence (PL), there exists exactly one such h if L is symmetric, and there exist exactly two such h if L is nonsymmetric. (2) ${\text {Fix}}(h)$ is disconnected only if $p \equiv 0 \bmod n$, and there exists exactly one such h up to weak equivalence (PL). A ${Z_n}$-action is called nonfree if ${\text {Fix}}(\phi ) \ne \emptyset$ for some $\phi ( \ne 1) \in {Z_n}$. We also classify all orientation-preserving nonfree ${Z_4}$-actions (PL) on all lens spaces $L(p,q)$. It follows that each of ${S^3}$ and ${P^3}$ admits exactly three orientation-preserving ${Z_4}$-actions (PL), up to conjugation.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S25
  • Retrieve articles in all journals with MSC: 57S25
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 237 (1978), 121-144
  • MSC: Primary 57S25
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0479366-5
  • MathSciNet review: 479366