关于逆映射类幺半群
On the inverse mapping class monoids
摘要：
辫群和映射类群具有许多共同的功能。类似于逆辫幺半群的概念，定义了逆映射类幺半群.它涉及具有穿孔的曲面，但在给定的$n$穿孔中，有几个可以省略。这对应于其中串的数量不固定的编织物。本文给出了Dehn-Nilsen-Baer定理的类似结果，给出了穿孔球面上逆映射类么半群的表示，并研究了字问题.这表明基于映射类群的某些性质和对象可以扩展到逆映射类幺半群。我们也给出了一个类似的Artin表示与两个生成元。
英文摘要：
Braid groups and mapping class groups have many features in common. Similarly to the notion of inverse braid monoid inverse mapping class monoid is defined. It concerns surfaces with punctures, but among given $n$ punctures several can be omitted. This corresponds to braids where the number of strings is not fixed. In the paper we give the analogue of the Dehn-Nilsen-Baer theorem, propose a presentation of the inverse mapping class monoid for a punctured sphere and study the word problem. This shows that certain properties and objects based on mapping class groups may be extended to the inverse mapping class monoids. We also give an analogues of Artin presentation with two generators.
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