Genus-two trisections are standard

摘要

We show that the only closed 4-manifolds admitting genus-two trisections are S-2 x S-2 and connected sums of S-1 x S-3, CP2 and (CP) over bar (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 tunnel number one links with an integral cosmetic Dehn surgery.