... Bcorresponding to the subgroup of 771(M-B)representedontopermutationswhichfix1,undthencompleting to f:N->Mbyfillingin the tubularneighborhood of B and extendingf' to f.Aregularbranchedcoveringisoneforwhichf':N') M - Bisaregu-larcovering,or inotherwords,oneforwhich the subgroup of 771(M-B)inquestionisnormal.Amongtheseare the cyclicbranchedcoverings,givenbyrepresentations771(M-B)->Znonto the cyclicgroup of ordern,suchthat the projectionf:N ... SYMMETRICFIBEREDLINKS9neighborhoodsTi of the ci's and regluing the closedneighborhoodsbyorientationpreservingself-homeomorphismscPi:aTi aTi of theirboundary.Itisnothard to seethatNisdeterminedup to homeomorphismby the homologyclasses of the imagecurvescPi(mi)inHI(aTi;Z),wheremiisameridianonaTi(i.e.,miisanorientedsimpleclosedcurveonaTiwhichspansadiskinT ... CisagainS3. To seethis,decomposeS3intotwosolidtorisharinga commonboundary, the tubularneighborhoodT I of C, and the complementarysolidtorusT2'Let1>:T2 T2bea homeomorphismwhichcarriesm to the curve~3 3mj-kE;thencPextends to a...