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Genus-two trisections are standard

2017; Mathematical Sciences Publishers; Volume: 21; Issue: 3 Linguagem: Inglês

10.2140/gt.2017.21.1583

1465-3060

Jeffrey Meier, Alexander Zupan,

semigroups and automata theory

We show that the only closed 4-manifolds admitting genus two trisections are S 2 ×S 2 and connected sums of S 1 ×S 3 , CP 2 , and CP 2 with two summands.Moreover, each of these manifolds admits a unique genus two trisection up to diffeomorphism.The proof relies heavily on the combinatorics of genus two Heegaard diagrams of S 3 .As a corollary, we classify two-component links contained in a genus two Heegaard surface for S 3 with a surface-sloped cosmetic Dehn surgery.