接触连通和下的支撑亏格不增加
The support genus does not increase under contact connected sum
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中文总结 AI 辅助
研究接触三维流形接触连通和的支撑亏格，证明其至多为被加项支撑亏格最大值，指出支撑亏格为一的接触流形迭代连通和支撑亏格至多为一，不能为更高支撑亏格接触流形提供候选。
中文摘要 AI 辅助
我们证明了两个接触三维流形的接触连通和的支撑亏格至多为被加项支撑亏格的最大值。特别地，支撑亏格为一的接触流形的迭代连通和的支撑亏格仍至多为一，因此不能为更高支撑亏格的接触流形提供候选。
英文摘要
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.
