The support genus does not increase under contact connected sum

Miguel Orbegozo Rodriguez; Eric Stenhede

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arXiv · 2607.19892

The support genus does not increase under contact connected sum

Miguel Orbegozo Rodriguez·Eric Stenhede

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Abstract

We show that the support genus of the contact connected sum of two contact $3$-manifolds is at most the maximum of the support genera of the summands. In particular, iterated connected sums of contact manifolds of support genus one still have support genus at most one, and therefore cannot provide candidates for contact manifolds of higher support genus.

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Miguel Orbegozo Rodriguez, Eric Stenhede. 2026-07-22. The support genus does not increase under contact connected sum. https://arxiv.org/abs/2607.19892

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