Topology Atlas
Document # ppae-22

## An intrinsic characterization of p-symmetric Heegaard splittings

### Michele Mulazzani

Proceedings of the Ninth Prague Topological Symposium
(2001)
pp. 217-222
We show that every p-fold strictly-cyclic branched covering of a
b-bridge link in **S**^{3} 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.

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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.

Copyright © 2002
Charles University and
Topology Atlas.
Published April 2002.