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.

 

Regular coverings of homology $3$-spheres by homology $3$-spheres
HTML articles powered by AMS MathViewer

by E. Luft and D. Sjerve PDF
Trans. Amer. Math. Soc. 311 (1989), 467-481 Request permission

Abstract:

We study $3$-manifolds that are homology $3$-spheres and which admit nontrivial regular coverings by homology $3$-spheres. Our main theorem establishes a relationship between such coverings and the canonical covering of the $3$-sphere ${S^3}$ onto the dodecahedral space ${D^3}$. We also give methods for constructing irreducible sufficiently large homology $3$-spheres $\tilde M,\;M$ together with a degree $1$ map $h:M \to {D^3}$ such that $\tilde M$ is the covering space of $M$ induced from the universal covering ${S^3} \to {D^3}$ by means of the degree $1$ map $h:M \to {D^3}$. Finally, we show that if $p:\tilde M \to M$ is a nontrivial regular covering and $\tilde M,\;M$ are homology spheres with $M$ Seifert fibered, then $\tilde M = {S^3}$ and $M = {D^3}$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 57N10, 57M10
  • Retrieve articles in all journals with MSC: 57N10, 57M10
Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 467-481
  • MSC: Primary 57N10; Secondary 57M10
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0978365-1
  • MathSciNet review: 978365