Connected sums of unstabilized Heegaard splittings are unstabilized
Connected sums of unstabilized Heegaard splittings are unstabilized
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DOI：
10.2140/gt.2008.12.2327
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发表时间：
2004-04
影响因子：
2
通讯作者：
D. Bachman
中科院分区：
文献类型：
--
作者：
D. Bachman
设M1和M2是闭的、可定向的三维流形。设Hi表示Mi中的Heegaard曲面。我们证明了如果H1#H2来自于稳定M1#M2的一个下亏格分裂，那么H1或H2中的一个来自于稳定一个下亏格分裂。这回答了C Gordon [9，Problem 3.91]的一个问题。我们还证明了每一个不稳定的Heegaard分裂都有一个唯一的表达式作为素3流形的Heegaard分裂的连通和。
Let M1 and M2 be closed, orientable 3‐manifolds. Let Hi denote a Heegaard surface in Mi . We prove that if H1#H2 comes from stabilizing a lower genus splitting of M1#M2 then one of H1 or H2 comes from stabilizing a lower genus splitting. This answers a question of C Gordon [9, Problem 3.91]. We also show that every unstabilized Heegaard splitting has a unique expression as the connected sum of Heegaard splittings of prime 3‐manifolds.