Regular coverings of homology -spheres by homology -spheres

Authors:
E. Luft and D. Sjerve

Journal:
Trans. Amer. Math. Soc. **311** (1989), 467-481

MSC:
Primary 57N10; Secondary 57M10

MathSciNet review:
978365

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Abstract: We study -manifolds that are homology -spheres and which admit nontrivial regular coverings by homology -spheres. Our main theorem establishes a relationship between such coverings and the canonical covering of the -sphere onto the dodecahedral space . We also give methods for constructing irreducible sufficiently large homology -spheres together with a degree map such that is the covering space of induced from the universal covering by means of the degree map . Finally, we show that if is a nontrivial regular covering and are homology spheres with Seifert fibered, then and .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1989-0978365-1

Keywords:
Homology -spheres,
coverings,
binary icosahedral group,
dodecahedral space,
degree maps

Article copyright:
© Copyright 1989
American Mathematical Society