Berge's distance 3 pairs of genus 2 Heegaard splittings
arXiv:1002.4887 · doi:10.1017/S0305004111000223
Abstract
Following an example discovered by John Berge, we show that there is a 4-component link L \subset (S^1 x S^2)#(S^1 x S^2) so that, generically, the result of Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard splittings, and each of these Heegaard splittings is of Hempel distance 3.
18 pages, 8 figures