An embedding of the Morse boundary in the Martin boundary

Complete topological descriptions of certain Morse boundaries

We study direct limits of embedded Cantor sets and embedded \sier curves. We show that under appropriate conditions on the embeddings, all limits of Cantor spaces give rise to homeomorphic spaces, called $ω$-Cantor spaces, and similarly, all limits of \sier curves give homeomorphic spaces, called to $ω$-\sier curves. We then show that the former occur naturally as Morse boundaries of right-angled Artin groups and fundamental groups of non-geometric graph manifolds, while the latter occur as Morse boundaries of fundamental groups of finite-volume, cusped hyperbolic 3-manifolds.

Embedding $\mathbb{Q}$ into a Finitely Presented Group

We observe that the group of all lifts of elements of Thompson's group $T$ to the real line is finitely presented and contains the additive group $\mathbb{Q}$ of the rational numbers. This gives an explicit realization of the Higman embedding theorem for $\mathbb{Q}$, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.

The Structure of Root Data and Smooth Regular Embeddings of Reductive Groups

We investigate the structure of root data by considering their decomposition as a product of a semisimple root datum and a torus. Using this decomposition we obtain a parameterisation of the isomorphism classes of all root data. By working at the level of root data we introduce the notion of a smooth regular embedding of a connected reductive algebraic group, which is a refinement of the commonly used regular embeddings introduced by Lusztig. In the absence of Steinberg endomorphisms such embeddings were constructed by Benjamin Martin. In an unpublished manuscript Asai proved three key reducti…

虚拟自由群的 Outer Space 之间的 Lipschitz 度量等距映射

Lipschitz metric isometries between Outer Spaces of virtually free groups

本文将自由群有限指数覆盖诱导的 Lipschitz 等距嵌入及折叠路径保持性推广到虚拟自由群，并证明距离候选存在性、建立其 Outer Space 脊与 Krstić–Vogtmann 空间的形变收缩关系。