Haimiao Chen

activity

20112023

most citedAutomorphisms of metacyclic groups

7 citations · 45 across the 32 of their papers we have counts for

collaborators

33 papers

math.GT2023

The $SL (2, C)$ -character variety of an arborescent knot

Haimiao Chen

We describe a procedure for computing the $SL (2, C)$ -character variety of an arborescent knot. Along the way, we clarify several facts about representations of arbore…

math.GT2023

Integral structure of the skein algebra of the 5-punctured sphere

Haimiao Chen

We give an explicit presentation for the Kauffman bracket skein algebra of the $5$ -punctured sphere over any commutative unitary ring.

math.GT2022

On skein algebras of planar surfaces

Haimiao Chen

Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ . Let $S_{n}$ denote the Kauffman bracket skein algebra of the $n$ -holed disk $Σ…

math.GR2022

A new approach to the genus spectra of abelian $p$ -groups

Haimiao Chen, Yang Li

Given a finite group $G$ , the {\it genus spetrum} $sp (G)$ of $G$ is the set of integers $g \geq 0$ such that $G$ can act faithfully on an orientable closed surface of genus $g…

math.GT2022

The $SL (2, C)$ -character variety of the Borromean link

Haimiao Chen, Tiantian Yu

For the Borromean link, we determine its irreducible $SL (2, C)$ -character variety, and find a formula for the twisted Alexander polynomial as a function on the charac…

math.GT2021★ 1 cited

Lifting homeomorphisms and finite abelian branched covers of the 2-sphere

Haimiao Chen

We completely determine finite abelian regular branched covers of the 2-sphere $S^{2}$ with the property that each homeomorphism of $S^{2}$ preserving the branching set can be lifted.

math.GT2021★ 2 cited

The $SL (2, C)$ -character variety of a Montesinos knot

Haimiao Chen

For each Montesinos knot $K$ , we propose an efficient method to explicitly determine the irreducible $SL (2, C)$ -character variety, and show that it can be decomposed…

math.GR2020★ 1 cited

Solving the isomorphism problems for two families of parafree groups

Haimiao Chen

For any integers $m, n$ with $m \neq = 0$ and $n > 0$ , let $G_{m, n}$ denote the group presented by $⟨ x, y, z ∣ x = [z^{m}, x] [z^{n}, y]⟩$ ; for any integers $m, n > 0$ , let $H_{m, n}$ den…

math.GR2020

Finite $p$ -groups of class $2$ as central extensions

Haimiao Chen

Finite $p$ -groups of nilpotency class 2 are treated from the perspective of central extensions. Given finite abelian groups $G, A$ , we derive an explicit formula for cocycles repres…

math.GT2019★ 1 cited

Cohomological invariants of representations of 3-manifold groups

Haimiao Chen

Suppose $Γ$ is a discrete group, and $α \in Z^{3} (B Γ; A)$ , with $A$ an abelian group. Given a representation $ρ : π_{1} (M) \to Γ$ , with $M$ a closed 3-manifold, put $F(M,ρ)=\langle(Bρ)^\ast[…

math.GT2018★ 3 cited

Character varieties of even classical pretzel knots

Haimiao Chen

For each even classical pretzel knot $P (2 k_{1} + 1, 2 k_{2} + 1, 2 k_{3})$ , we determine the character variety of irreducible $SL (2, C)$ -representations, and clarify the steps of c…

math.GT2018

$SL (3, C)$ -character varieties of two-generator groups

Haimiao Chen

We present an efficient method for computing the $SL (3, C)$ -character varieties of two-generator groups.

math.GT2018★ 1 cited

On the groups of periodic links

Haimiao Chen

It is shown that, if a link $L ~ \subset S^{3}$ is $p^{k}$ -periodic with $p$ prime and $k \geq 1$ , and $L$ is the quotient link, then the groups of $L ~$ and $L$ can be relate…

math.RT2018

Representation category of the quantum double of $SL (2, q)$

Haimiao Chen

For each odd prime power $q$ with $q \geq 5$ and $4 ∣ q - 1$ , we investigate the structure of the representation category of the quantum double of $SL (2, q)$ , determining its te…

math.GT2017

Alexander polynomial, Dijkgraaf-Witten invariant, and Seifert fibred surgery

Haimiao Chen

We apply Dijkgraaf-Witten invariant over an semiproduct of abelian groups to show that, if the $k / ℓ$ -surgery along a knot $K$ results in a small Seifert 3-manifold with multipli…

math.GT2017★ 2 cited

Computing twisted Alexander polynomials for Montesinos links

Haimiao Chen

In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For Montesinos links, we develop an efficient method to compute the tw…

math.GT2017

Trace-free $SL (2, C)$ -representations of arborescent links

Haimiao Chen

Given a link $L \subset S^{3}$ , a representation $π_{1} (S^{3} - L) \to SL (2, C)$ is {\it trace-free} if it sends each meridian to an element with trace zero. We present a method…

math.GR2017

The automorphism group of a nonsplit metacyclic 2-group

Haimiao Chen

We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$ -groups.

math.GT2017★ 6 cited

Character varieties of odd classical pretzel knots

Haimiao Chen

We determine the $SL (2, C)$ -character variety for each odd classical pretzel knot $P (2 k_{1} + 1, 2 k_{2} + 1, 2 k_{3} + 1)$ , and present a method for computing its A-polynomial.

math.CO2017

Regular $t$ -balanced Cayley maps on split metacyclic $2$ -groups

Haimiao Chen, Jingrui Zhang

A regular $t$ -balanced Cayley map on a group $Γ$ is an embedding of a Cayley graph on $Γ$ into a surface with certain special symmetric properties. We completely classify regular $…

math.GT2016★ 3 cited

Tracefree $SL (2, C)$ -representations of Montesinos links

Haimiao Chen

Given a link $L$ , a representation $π_{1} (S^{3} - L) \to SL (2, C)$ is {\it tracefree} if the image of each meridian has trace zero. We determine the conjugacy classes of t…

math.CO2016

Regular balanced Cayley maps on $PSL (2, p)$

Haimiao Chen

A {\it regular balanced Cayley map} (RBCM for short) on a finite group $Γ$ is an embedding of a Cayley graph on $Γ$ into a surface, with some special symmetric property. People hav…

math.GR2015★ 7 cited

Automorphisms of metacyclic groups

Haimiao Chen, Yueshan Xiong, Zhongjian Zhu

A metacyclic group $H$ can be presented as $⟨ α, β ∣ α^{n} = 1, β^{m} = α^{t}, β α β^{- 1} = α^{r} ⟩$ for some $n, m, t, r$ . Each endomorphism $σ$ of $H$ is determined by $σ(α)…

math.CO2014★ 1 cited

Quotients of polynomial rings and regular t-balanced Cayley maps on abelian groups

Haimiao Chen

Given a finite group $Γ$ , a regular $t$ -balanced Cayley map (RBCM $_{t}$ for short) is a regular Cayley map $CM (G, Ω, ρ)$ such that $ρ (ω)^{- 1} = ρ^{t} (ω)$ for all $ω \in Ω$ . In…

The SL(2,C)-character variety of an arborescent knot

Integral structure of the skein algebra of the 5-punctured sphere

On skein algebras of planar surfaces

A new approach to the genus spectra of abelian p-groups

The SL(2,C)-character variety of the Borromean link

Lifting homeomorphisms and finite abelian branched covers of the 2-sphere

The SL(2,C)-character variety of a Montesinos knot

Solving the isomorphism problems for two families of parafree groups

Finite p-groups of class 2 as central extensions

Cohomological invariants of representations of 3-manifold groups

Character varieties of even classical pretzel knots

SL(3,C)-character varieties of two-generator groups

On the groups of periodic links

Representation category of the quantum double of SL(2,q)

Alexander polynomial, Dijkgraaf-Witten invariant, and Seifert fibred surgery

Computing twisted Alexander polynomials for Montesinos links

Trace-free SL(2,C)-representations of arborescent links

The automorphism group of a nonsplit metacyclic 2-group

Character varieties of odd classical pretzel knots

Regular t-balanced Cayley maps on split metacyclic 2-groups

Tracefree SL(2,C)-representations of Montesinos links

Regular balanced Cayley maps on PSL(2,p)

Automorphisms of metacyclic groups

Quotients of polynomial rings and regular t-balanced Cayley maps on abelian groups

The $SL (2, C)$ -character variety of an arborescent knot

A new approach to the genus spectra of abelian $p$ -groups

The $SL (2, C)$ -character variety of the Borromean link

The $SL (2, C)$ -character variety of a Montesinos knot

Finite $p$ -groups of class $2$ as central extensions

$SL (3, C)$ -character varieties of two-generator groups

Representation category of the quantum double of $SL (2, q)$

Trace-free $SL (2, C)$ -representations of arborescent links

Regular $t$ -balanced Cayley maps on split metacyclic $2$ -groups

Tracefree $SL (2, C)$ -representations of Montesinos links

Regular balanced Cayley maps on $PSL (2, p)$