论文标题
dehn Quandles表面的规范商的有限性
Finiteness of canonical quotients of Dehn quandles of surfaces
论文作者
论文摘要
封闭的可定向表面的dehn Quandle是一组非分离的简单闭合曲线的同位素类别，其自然拼布结构是由Dehn Twist产生的。在本文中，我们考虑了这些难题的某些规范商的有限。对于阳性属的表面，我们对其dehn Quandle的2 Quandle进行了精确描述。此外，除了两个以上的属外，我们确定了$ n $的所有值，其$ n $ quandle的dehn Quandle都是有限的。可以将结果视为Hoste和Shanahan的类似结果的Dehn Quandle类似物。我们还计算了表面的dehn Quandle的最小非平凡拼图商的大小。在此过程中，我们证明了Artin Quandle的in象商恰恰是相应的Coxeter Quandle，并且还确定了编织式公寓的最小非平凡商。
The Dehn quandle of a closed orientable surface is the set of isotopy classes of non-separating simple closed curves with a natural quandle structure arising from Dehn twists. In this paper, we consider finiteness of some canonical quotients of these quandles. For a surface of positive genus, we give a precise description of the 2-quandle of its Dehn quandle. Further, with some exceptions for genus more than two, we determine all values of $n$ for which the $n$-quandle of its Dehn quandle is finite. The result can be thought of as the Dehn quandle analogue of a similar result of Hoste and Shanahan for link quandles. We also compute the size of the smallest non-trivial quandle quotient of the Dehn quandle of a surface. Along the way, we prove that the involutory quotient of an Artin quandle is precisely the corresponding Coxeter quandle and also determine the smallest non-trivial quotient of a braid quandle.
