Brieskorn Manifolds, Generalized Sieradski Groups, and Coverings of Lens Spaces Full article
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Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 , E-ISSN: 1531-8605 |
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| Output data | Year: 2019, Volume: 304, Pages: S175-S185 Pages count : DOI: 10.1134/S0081543819020196 | ||||||
| Tags | 3-manifold; branched covering; Brieskorn manifold; cyclically presented group; lens space; Sieradski group | ||||||
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Abstract:
A Brieskorn manifold B(p, q, r) is the r-fold cyclic covering of the 3-sphere S3 branched over the torus knot T(p, q). Generalized Sieradski groups S(m, p, q) are groups with an m-cyclic presentation Gm(w), where the word w has a special form depending on p and q. In particular, S(m, 3, 2) = Gm(w) is the group with m generators x1,…, xm and m defining relations w(xi, xi+1, xi+2) = 1, where w(xi, xi+1, xi+2) = xi, xi+2, xi+1−1. Cyclic presentations of the groups S(2n, 3, 2) in the form Gn(w) were investigated by Howie and Williams, who showed that the n-cyclic presentations are geometric, i.e., correspond to spines of closed 3-manifolds. We establish a similar result for the groups S(2n, 5, 2). It is shown that in both cases the manifolds are n-fold branched cyclic coverings of lens spaces. To classify some of the constructed manifolds, we use Matveev’s computer program “Recognizer”. © 2019, Pleiades Publishing, Ltd.
Cite:
Vesnin A.Y.
, Kozlovskaya T.A.
Brieskorn Manifolds, Generalized Sieradski Groups, and Coverings of Lens Spaces
Proceedings of the Steklov Institute of Mathematics. 2019. V.304. P.S175-S185. DOI: 10.1134/S0081543819020196 WOS Scopus OpenAlex
Brieskorn Manifolds, Generalized Sieradski Groups, and Coverings of Lens Spaces
Proceedings of the Steklov Institute of Mathematics. 2019. V.304. P.S175-S185. DOI: 10.1134/S0081543819020196 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000470756500018 |
| Scopus: | 2-s2.0-85067065539 |
| OpenAlex: | W2754455881 |