关于曲面映射类群的自同态

映射环面的自同态

Endomorphisms of mapping tori

本文利用Hopf型性质对非零欧拉示性数的剩余有限Poincaré对偶群的映射环面进行分类，推广了纤维化3流形的相关结果，并证明了Gromov双曲群的刚性结果对具有平凡中心的映射环面成立。

Big mapping class groups and the co-Hopfian property

We study injective homomorphisms between big mapping class groups of infinite-type surfaces. First, we construct (uncountably many) examples of surfaces without boundary whose (pure) mapping class groups are not co-Hopfian; these are the first examples of injective endomorphisms of mapping class groups (of surfaces with empty boundary) that fail to be surjective. We then prove that, subject to some topological conditions on the domain surface, any continuous injective homomorphism between (arbitrary) big mapping class groups that sends Dehn twists to Dehn twists is induced by homeomorphism. Fi…

代数熵与映射类群在Character簇上的作用

Algebraic Entropy and the Action of Mapping Class Groups on Character Varieties

我们将代数熵的定义推广到仿射簇的自同态。我们计算了映射类群的元素在各种特征簇上的作用的代数熵，并证明了它等于一个我们称之为谱半径的量，它是伪Anosov映射类伸缩的推广.我们的计算是兼容的所有已知的计算拓扑熵的这种行动。

自由阿贝尔乘曲面群中自同态的不动子群分类

Classification of Fixed Subgroups of Endomorphisms in Free-abelian Times Surface Groups

本文研究自由阿贝尔乘曲面群等群类的自同态性质，刻画其自同态双射条件，证明相关群的Hopf性，完成自同态不动子群完整分类并给出有限不动子群的等价条件。

环群上的混合自同态及其可数积

Mixing endomorphisms on toroidal groups and their countable products

我们证明了循环群的所有非平凡连续自同态都是拓扑混合的。我们还证明了任意n维环面群都存在一个无穷大类拓扑混合的连续自同态。最后证明了具有单位元的阿贝尔波兰半群上的连续自同态可以自然地推广到该半群的可数无穷乘积上的拓扑混合自同态。证明了阿贝尔Polish半群的每一个可数无穷乘积都有一个拓扑混合自同态，特别是可数无限环群有无穷多个拓扑混合自同态。

剩余有限与投射quandle的自同态幺半群与自同构群

Endomorphism monoid and automorphism group of residually finite and profinite quandles

该研究探讨剩余有限与投射quandle，证明有限生成及一大类剩余有限quandle的自同态幺半群、自同构群为剩余有限，给出投射quandle拓扑刻画并建立其自同态幺半群与自同构群为投射的充要条件。