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arXiv 1902.06388math.GT
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具有边界的纤维3-流形的平移距离界

Translation distance bounds for fibered 3-manifolds with boundary

Alexander Stas

摘要:

给定$M_φ$,一个带边界的纤维3-流形,我们证明了单值$φ$的平移距离可以由具有非零斜率的本质曲面的复杂性上界。进一步证明了$M_{φ^n}$中非零斜率曲面的最小复杂度趋于无穷大,即$n\to\infty$。此外,我们表明,纤维双曲结的无限家庭的平移距离上界为2,满足Schleimer的猜想,假设这种行为应该持有所有纤维结。

英文摘要:

Given $M_φ$, a fibered 3-manifold with boundary, we show that the translation distance of the monodromy $φ$ can be bounded above by the complexity of an essential surface with non-zero slope. Furthermore we prove that the minimal complexity of a surface with non-zero slope in $M_{φ^n}$ tends to infinity as $n\to\infty$. Additionally, we show that an infinite family of fibered hyperbolic knots has translation distance bounded above by two, satisfying a conjecture by Schleimer which postulates that this behavior should hold for all fibered knots.

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