Grasselli, Luigi; Mulazzani, Michele Seifert manifolds and (1,1)-knots. (Russian, English) Zbl 1224.57004 Sib. Mat. Zh. 50, No. 1, 28-39 (2009); translation in Sib. Math. J. 50, No. 1, 22-31 (2009). Summary: We study the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that each orientable Seifert manifold with invariants \[ \{Oo, 0 \;| -1; \underbrace{(p,q),\dots,(p,q)}_{n\;\text{times}},(l,l-1)\} \] has a fundamental group cyclically presented by \(G_n((x_1^q\dots x_n^q)^l x_n^{-p})\), and, moreover, it is the \(n\)-fold strongly-cyclic covering of the lens space \(L(| nlq-p| , q)\) which is branched over the (1,1)-knot \(K(q, q(nl-2), p-2q, p-q)\) if \(p\geq 2q\) and over the (1,1)-knot \(K(p-q, 2q-p, q(nl-2), p-q)\) if \(p<2q\). Cited in 2 Documents MSC: 57M50 General geometric structures on low-dimensional manifolds 57M05 Fundamental group, presentations, free differential calculus 57M25 Knots and links in the \(3\)-sphere (MSC2010) Keywords:Seifert manifold; (1,1)-knot; cyclic branched covering; cyclically presented group; Heegaard diagram PDFBibTeX XMLCite \textit{L. Grasselli} and \textit{M. Mulazzani}, Sib. Mat. Zh. 50, No. 1, 28--39 (2009; Zbl 1224.57004); translation in Sib. Math. J. 50, No. 1, 22--31 (2009) Full Text: arXiv EuDML EMIS