Francis Wagner
We construct the first examples of finitely presented groups with cubic Dehn function containing a finitely generated infinite torsion subgroup. Moreover, we show that any infinite free Burnside group with sufficiently large odd exponent can be embedded as a subgroup of a finitely presented group with cubic Dehn function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We construct the first examples of finitely presented groups with quadratic Dehn function containing a finitely generated infinite torsion subgroup. These examples are "optimal" in the sense that the Dehn function of any such finitely presented group must be at least quadratic. Moreover, we show that for any $n\geq2^{48}$ such that $n$ is either odd or divisible by $2^9$, any infinite free Burnside group with exponent $n$ is a quasi-isometrically embedded subgroup of a finitely presented group with quadratic Dehn function satisfying the Congruence Extension Property.
Baumslag's group is a finitely presented metabelian group with a Z \wr Z subgroup. There is an analogue with an additional torsion relation in which this subgroup becomes C_m \wr Z. We prove that Baumslag's group has an exponential Dehn function. This contrasts with the torsion analogues which have quadratic Dehn functions. v.2: version for publication, incorporating referee's suggestions.
A generalized torsion element is a non-trivial element such that some non-empty finite product of its conjugates is the identity. We construct a generalized torsion element of the fundamental group of a 3-manifold obtained by Dehn surgery along a knot in the 3-sphere.
We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.
We prove that if the Cayley graph of a finitely generated group enjoys the property L_delta then the group is almost convex and has a sub-cubic isoperimetric function.
Let $Γ$ be a finite simplicial graph such that the flag complex on $Γ$ is a $2$-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated Bestvina--Brady group is either quadratic, cubic, or quartic. Furthermore, we can identify the Dehn function from the defining graph $Γ$.
We show that the Dehn function of the handlebody group is exponential in any genus $g\geq 3$. On the other hand, we show that the handlebody group of genus $2$ is cubical, biautomatic, and therefore has a quadratic Dehn function.
A homogeneous nilpotent Lie group has a scaling automorphism determined by a grading of its Lie algebra. Many proofs of upper bounds for the Dehn function of such a group depend on being able to fill curves with discs compatible with this grading; the area of such discs changes predictably under the scaling automorphism. In this paper, we present combinatorial methods for finding such bounds. Using this method, we give new proofs of some results on Dehn functions of nilpotent groups, prove theorems on central powers and certain quotients of nilpotent groups, and construct the first example of …
We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups) by congruences, and the mixed Whitehead problem, an automorphism group orbit problem. The first step of the reduction is to compute canonical JSJ decompositions. Dehn fillings and the given solutions of the algorithmic problems in the parabolic groups are then used to decide if…
We address the problem of which functions can arise as Dehn functions of Kähler groups. We explain why there are examples of Kähler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a Kähler group which has Dehn function bounded below by a cubic function and above by $n^6$. As a consequence we obtain that for a compact Kähler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.
We show, under mild hypotheses, that if each element of a finitely generated group acting on a $2$-dimensional $\mathrm{CAT}(0)$ complex has a fixed point, then there is a global fixed point. In particular all actions of finitely generated torsion groups on such complexes have global fixed points. The proofs rely on Masur's theorem on periodic trajectories in rational billiards, and Ballmann-Brin's methods for finding closed geodesics in $2$-dimensional locally $\mathrm{CAT}(0)$ complexes. As another ingredient we prove that the image of an immersed loop in a graph of girth $2π$ with length no…
Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups
研究无挠双曲群中纤维积的共轭问题复杂性，通过建立不等式，将纤维积的共轭长度函数与\(Q\)中循环子群几何等联系起来，为扩展相关函数库提供工具。
Complete classification of the Dehn functions of Bestvina-Brady groups
本文证明了每个有限表示的Bestvina-Brady群的Dehn函数增长为线性、二次、三次或四次多项式，并给出了确定多项式次数的显式判据，进而识别了阻碍某些Bestvina-Brady群具有CAT(0)结构的障碍。
Cusped spaces for hierarchically hyperbolic groups, and applications to Dehn filling quotients
本文提出一种构造方法，同时产生相对超几何群的漏斗空间和准等距于泰克米勒度量的空间。通过此方法研究了各种群的德恩填充类似商，包括穿孔球的映射类群。特别地，证明了五孔球的映射类群（或四strand辫群）有无限超几何商，且不与其他球面映射类群（或辫群）的超几何商同构。
Conjugator Lengths and Isoperimetric functions
该研究构造了有限表示群，揭示共轭子长度函数与Dehn函数这两个不变量具有强独立性，还给出了共轭子长度函数递归但字、共轭问题均不可判定的首个例子。
Dehn filling and the knot group II: Ubiquity of persistent elements
研究非平凡结的Dehn填充下持久元素的存在性，证明每非平凡结群中存在无限多个持久元素，且这些元素在群结构中广泛分布。
Torsion in the homology of the Torelli group and the Birman-Craggs-Johnson homomorphism
本文研究Torelli群同调群中由分离简单闭曲线的Dehn扭转生成的abelian cycle，证明在k≤g-2时，这些cycle在Birman-Craggs-Johnson同态下的像线性无关。
Weak commutativity, virtually nilpotent groups, and Dehn functions
本文研究弱交换构造 $\mathfrak{X}(G)$，通过分析正规交换子群模结构，证明其保持虚拟幂零、Engel 与增长类型，并刻画字问题及 Dehn 函数下界。
On Dehn functions for infinite group presentations
研究有限生成集但可能无限定义关系的群表示中Dehn函数的渐近行为，通过构造具体例子（如自由阿贝尔群Z^2）展示无限表示可产生连续统多种不同的精细填充增长行为。
The 3-strand braid group with torsion
本文通过轨道形形式体系为带挠率的三股辫群提供拓扑解释，揭示其与柏拉图立体之间的结构联系，弥补了Coxeter有限逐例检验证明的不足。
We give a solution to Dehn's isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for groups with peripheral structures. As a corollary, we give a uniform solution to Whitehead's problem asking whether two tuples of elements of a hyperbolic group $G$ are in the same orbit under the action of $\Aut(G)$. We also get an algorithm computing a generating set of the group of automorphisms of a hyperbolic group preserving a peripheral structure.
Dimensions of finitely generated simple groups and their subgroups
本文构造了具有强同调控制的有限生成单的无挠群，证明几乎所有维数集合都可实现为其子群维数集合，并首次给出维数不为2或∞的有限生成单群例子，方法结合小消去理论与Dehn填充。
On the non-triviality of the torsion subgroup of the abelianized Johnson kernel
本文通过二维方法证明了abelized Johnson核的torsion子群非平凡，并给出了其基数的下界。
On torsion in the homology of the Torelli group
本文研究Torelli群同调中由分离简单闭曲线的Dehn扭转生成的abelian cycles，证明它们构成Z/2Z-向量空间，且在k=2且g≥4时有限维。
A previous work of A. Conway and the author introduced $L^2$-Burau maps of braids, which are generalizations of the Burau representation whose coefficients live in a more general group ring than the one of Laurent polynomials. This same work established that the $L^2$-Burau map of a braid at the group of the braid closure yields the $L^2$-Alexander torsion of the braid closure in question, as a variant of the well-known Burau-Alexander formula. In the present paper, we generalize the previous result to $L^2$-Burau maps defined over all quotients of the group of the braid closure. The link inva…
A cubical Rips construction
本文提出一种立方Rips构造方法，在给定有限展示群和紧致特殊立方复形下，构造出满足特定上同调维数不等式且满射到原群的无挠双曲立方群。
Power quotients of surface groups and mapping class groups
本文研究闭双曲曲面基本群的幂商，证明其外自同构群与映射类群商群的同构，并揭示该商群的结构性质。
In the first part of this paper we prove that the mapping class subgroups generated by the $D$-th powers of Dehn twists (with $D\geq 2$) along a sparse collection of simple closed curves on an orientable surface are right angled Artin groups. The second part is devoted to power quotients, i.e. quotients by the normal subgroup generated by the $D$-th powers of all elements of the mapping class groups. We show first that for infinitely many $D$ the power quotient groups are non-trivial. On the other hand, if $4g+2$ does not divide $D$ then the associated power quotient of the mapping class group…
For some $g \geq 3$, let $Γ$ be a finite index subgroup of the mapping class group of a genus $g$ surface (possibly with boundary components and punctures). An old conjecture of Ivanov says that the abelianization of $Γ$ should be finite. In this note, we prove two theorems supporting this conjecture. For the first, let $T_x$ denote the Dehn twist about a simple closed curve $x$. For some $n \geq 1$, we have $T_x^n \in Γ$. We prove that $T_x^n$ is torsion in the abelianization of $Γ$. Our second result shows that the abelianization of $Γ$ is finite if $Γ$ contains a "large chunk" (in a certain…
Real Rational Surface Automorphisms : Positivity and Linearity
本文研究保持尖点三次曲线的实有理曲面自同构，通过自由基本群中的正半群与本原转移矩阵证明其正拓扑熵，并在 m+n 为奇数时给出伪 Anosov 实现。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。