arXiv subjects

Hang Lu Su

Publications and source records attributed to Hang Lu Su.

4 recordsLinked to original sources

arXiv2026

Finitely generated positive cones in $F_n \times \mathbb{Z}$

We construct, for every even $n \ge 2$, a positive cone on $F_n \times \mathbb{Z}$ that is finitely generated as a semigroup, extending the previously known construction for $n = 2$. Malicet, Mann, Rivas and Triestino proved that $F_n \times \mathbb{Z}$ admits an isolated left-order if and only if $n$ is even. Since every finitely generated positive cone determines an isolated left-order, for $n \ge 2$, the group $F_n \times \mathbb{Z}$ admits a finitely generated positive cone if and only if $n$ is even.

math.GR↗

arXiv2025

A toolbox for left-orders of low complexity

This thesis explores how concepts of formal language theory can be used to study left-orderable groups. It analyses the languages formed by their positive cones and demonstrates how the abstract families of languages (AFLs) in the Chomsky hierarchy (in particular regular and context-free languages) interact with core group-theoretic constructions under subgroups, extensions, finite generation and taking direct products with $\mathbb{Z}$. These investigations yield new insights into the interplay between decidability and geometry in group theory. Some results which may be improvements to the existing literature are included in the thesis. There is a classification of the complexity of positive cones of $\mathbb{Z}^2$, a more constructive proof on finding regular positive cone languages of language-convex subgroups compared to a result of Su (2020), a construction of countably infinite many regular positive cones of $\mathrm{BS}(1,q)$ for $q \geq -1$ which are all automorphic to each other extending a result of Antolín, Rivas, and Su (2022), and a construction of positive cones with finite generating set for groups of the form $F_{2n} \times \mathbb{Z}$ extending a result of Malicet, Mann, Rivas, and Triestino (2019).

math.GR↗

arXiv2021

Regular left-orders on groups

A regular left-order on finitely generated group $G$ is a total, left-multiplication invariant order on $G$ whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. We show that admitting regular left-orders is stable under extensions and wreath products and give a classification of the groups all whose left-orders are regular left-orders. In addition, we prove that solvable Baumslag-Solitar groups $B(1,n)$ admits a regular left-order if and only if $n\geq -1$. Finally, Hermiller and Sunic showed that no free product admits a regular left-order, however we show that if $A$ and $B$ are groups with regular left-orders, then $(A*B)\times \mathbb{Z}$ admits a regular left-order.

math.GR↗

arXiv2020

Formal language convexity in left-orderable groups

We propose a criterion for preserving the regularity of a formal language representation when passing from groups to subgroups. We use this criterion to show that the regularity of a positive cone language in a left-orderable group passes to its finite index subgroups, and to show that there exists no left order on a finitely generated acylindrically hyperbolic group such that the corresponding positive cone is represented by a quasi-geodesic regular language. We also answer one of Navas' questions by giving an example of an infinite family of groups which admit a positive cone that is generated by exactly $k$ generators, for every $k \geq 3$. As a special case of our construction, we obtain a finitely generated positive cone for $F_2 \times \mathbb{Z}$.

math.GR↗