Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors
Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors
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伪阿诺索夫拉伸因子的代数度和伽罗瓦共轭
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发表时间：
2015
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通讯作者：
Bal'azs Strenner
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作者：
Bal'azs Strenner
我们证明了Teichm-uller空间的每一个至多为维数的偶数正整数都是可定向曲面上伪Anosov伸缩因子的极小多项式的次数.根据瑟斯顿的度数上限，这些都是可能出现的偶数度数。我们证明了一个类似的结果，伪Anosov映射类定向不变的叶理。
我们还表明，从Penner的建设所产生的伪Anosov拉伸因子的伽罗瓦共轭是密集的复平面。这补充了较早的结果申和作者指出，这种伽罗瓦共轭可能永远不会躺在单位圆。
We show that every even positive integer at most the dimension of Teichm\"uller space occurs as the degree of the minimal polynomial of a pseudo-Anosov stretch factor on an orientable surface. By Thurston's upper bound on the degree, these are all the even degrees that may occur. We prove an analogous result for pseudo-Anosov mapping classes with orientable invariant foliations as well.
We also show that Galois conjugates of pseudo-Anosov stretch factors arising from Penner's construction are dense in the complex plane. This complements an earlier result of Shin and the author stating that such Galois conjugates may never lie on the unit circle.