We show that every p-fold strictly-cyclic branched covering of a b-bridge link in S3 admits a p-symmetric Heegaard splitting of genus g=(b-1)(p-1). This gives a complete converse to a result of Birman and Hilden, and gives an intrinsic characterization of p-symmetric Heegaard splittings as p-fold strictly-cyclic branched coverings of links.
Mathematics Subject Classification. 57M12 57R65 (20F05 57M05 57M25).
Keywords. 3-manifolds, Heegaard splittings, cyclic branched coverings, links, plats, bridge number, braid number.
Comments. This contribution is extracted from M. Mulazzani, On p-symmetric Heegaard splittings, J. Knot Theory Ramifications 9 (2000), no. 8, 1059-1067. Reprinted with permission from World Scientific Publishing Co.