论文标题
Kirby-Thompson距离的距离
Kirby-Thompson distance for trisections of knotted surfaces
论文作者
论文摘要
我们调整了Kirby-Thompson和Zupan的工作，以定义一个整数不变$ \ Mathcal {l}（\ Mathcal {t}）$的桥梁Trisection $ \ Mathcal {T Mathcal {t} $的光滑表面$ \ Mathcal $ \ Mathcal {k} $ in $ s^4 $或$ b^4 $。我们表明，当$ \ Mathcal {l}（\ Mathcal {t}）= 0 $时，Surface $ \ Mathcal {K} $未打结。我们还显示，对于不可约的表面的三角$ \ MATHCAL {T} $，桥号为$ \ MATHCAL {l}（\ MATHCAL {T}）$产生下限。因此，$ \ Mathcal {l} $可以任意大。
We adapt work of Kirby-Thompson and Zupan to define an integer invariant $\mathcal{L}(\mathcal{T})$ of a bridge trisection $\mathcal{T}$ of a smooth surface $\mathcal{K}$ in $S^4$ or $B^4$. We show that when $\mathcal{L}(\mathcal{T})=0$, then the surface $\mathcal{K}$ is unknotted. We also show show that for a trisection $\mathcal{T}$ of an irreducible surface, bridge number produces a lower bound for $\mathcal{L}(\mathcal{T})$. Consequently, $\mathcal{L}$ can be arbitrarily large.
