论文标题
有限的刚性套件在球体中
Finite rigid sets in sphere complexes
论文作者
论文摘要
如果每个本地注入式的，简单的映射$ x \ to \ Mathcal {c} $是限制$ \ Mathcal {c} $的唯一自动形态，则简单复合体的子复合$ x \ leq \ mathcal {c} $都是很僵硬的。 Aramayona和第二作者证明，有限的刚性集合可以用来耗尽定向表面的曲线复合体。 Hatcher Sphere Complex是曲线复合体的类似物，用于$ s^1 \ times s^2 $的连接总和的同位素类别类别。我们表明，对于所有$ n \ ge 3 $，有限刚性设置使球体复合体耗尽，当$ n = 2 $时，球体复合体没有有限的刚性套件。
A subcomplex $X\leq \mathcal{C}$ of a simplicial complex is strongly rigid if every locally injective, simplicial map $X\to\mathcal{C}$ is the restriction of a unique automorphism of $\mathcal{C}$. Aramayona and the second author proved that the curve complex of an orientable surface can be exhausted by finite strongly rigid sets. The Hatcher sphere complex is an analog of the curve complex for isotopy classes of essential spheres in a connect sum of $n$ copies of $S^1\times S^2$. We show that there is an exhaustion of the sphere complex by finite strongly rigid sets for all $n\ge 3$ and that when $n=2$ the sphere complex does not have finite rigid sets.
