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Surface cubications mod flips

Abstract

Let Σ\Sigma be a compact surface. We prove that the set of surface cubications modulo flips, up to isotopy, is in one-to-one correspondence with Z/2Z⊕H1(Σ,Z/2Z)\Z/2\Z\oplus H_1(\Sigma,\Z/2\Z).Comment: revised version, 18

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