On p-symmetric Heegaard splittings

Details On p-symmetric Heegaard splittings On p-symmetric Heegaard splittings

2000-07-26

arxiv.org/abs/math/0007162v1

Mathematics

Geometric Topology

11 pages, 2 figures, to appear in the Journal of Knot Theory and its Ramifications

Scientific paper

We show that every p-fold strictly-cyclic branched covering of a b-bridge link in $S^3$ admits a p-symmetric Heegaard splitting - in the sense of Birman and Hilden - of genus $g=(b-1)(p-1)$. This gives a complete converse of one of the results of the two authors. Moreover, we introduce the concept of weakly p-symmetric Heegaard splittings and prove similar results in this more general context.

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