2000/03/07 by Luigi Grasselli, Grasselli, Luigi, Michele Mulazzani +1
Mathematics · #20F05 #57M05 (Secondary) #57M12 #57M25 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20F05 #msc:57M05 #msc:57M12 #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0003042
24 pages, 10 figures
arxiv created 2000/03/07 · arxiv updated 2009/11/30
In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (eventually \bf S3), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of \bf S3 branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-bridge knot belong to this subclass; this implies that the fundamental group of each branched cyclic covering of a 2-bridge knot admits a geometric cyclic presentation.