Abstract

Harer-Kas-Kirby conjectured that every handle decomposition of the elliptic surface E(1)2,3 requires both 1- and 3-handles. We prove that the elliptic surface E(n)p,q has a handle decomposition without 1-handles for n ≥ 1 and (p, q) = (2, 3), (2, 5), (3, 4), (4, 5).

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