The structure of a solvmanifold's Heegaard splittings
The structure of a solvmanifold's Heegaard splittings
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发表时间：
1998-03
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通讯作者：
D. Cooper;M. Scharlemann
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作者：
D. Cooper;M. Scharlemann
我们对solvmanifolds不可约的Heegaard分裂进行了分类。如果可以将溶剂策略的单肌表示为2 x 2矩阵，右下角0（当痕迹的绝对值为3时，与往常一样为true），那么任何不可约定的分裂都是强烈不可约性的，而属二。如果此外，迹线的绝对值为4或更大，则任何两个这样的分裂都是同位素。如果迹线的绝对值为3，则直到同位素，恰好有两个不可还原的分裂，它们相关的过椭圆形相互作用通勤，而参与的乘积是Solvmanifold的核心涉及。如果单轨道不能表示为2 x 2矩阵，右下角为0，则分裂弱还原为三属，而唯一的同位素。
We classify isotopy classes of irreducible Heegaard splittings of solvmanifolds. If the monodromy of the solvmanifold can be expressed as a 2 x 2 matrix with 0 in the lower right hand corner (as always is true when the absolute value of the trace is 3), then any irreducible splitting is strongly irreducible and of genus two. If furthermore the absolute value of the trace is 4 or greater, then any two such splittings are isotopic. If the absolute value of the trace is 3 then, up to isotopy, there are exactly two irreducible splittings, their associated hyperelliptic involutions commute, and the product of the involutions is the central involution of the solvmanifold. If the monodromy cannot be expressed as a 2 x 2 matrix with 0 in the lower right hand corner, then the splitting is weakly reducible, of genus three and unique up to isotopy.