2005/10/15 by Luigi Grasselli, Grasselli, Luigi, Michele Mulazzani +1
Mathematics · #57M12 #57M25 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M12 #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0510318
20 pages, 17 figures
arxiv created 2005/10/15 · openalex publication_date 2005/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to investigate the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that every orientable Seifert manifold with invariants Oo,0|-1;(p,q),...,(p,q),(l, l-1) has a cyclically presented fundamental group and, moreover, it is the n-fold strongly-cyclic covering of the lens space L(|nlq-p|,q), branched over the (1,1)-knot K(q,q(nl-2),p-2q,p-q) if p>=2q, and over the (1,1)-knot K(p-q,2q-p,q(nl-2),p-q) if p<2q.