arXiv subjects

Dongping Zhuang

Publications and source records attributed to Dongping Zhuang.

3 recordsLinked to original sources

arXiv2011

Stable W-length

We study stable W-length in groups, especially for W equal to the n-fold commutator gamma_n:=[x_1,[x_2, . . . [x_{n-1},x_n]] . . . ]. We prove that in any perfect group, for any n at least 2 and any element g, the stable commutator length of g is at least as big as 2^{2-n} times the stable gamma_n-length of g. We also establish analogues of Bavard duality for words gamma_n and for beta_2:=[[x,y],[z,w]]. Our proofs make use of geometric properties of the asymptotic cones of verbal subgroups with respect to bi-invariant metrics. In particular, we show that for suitable W, these asymptotic cones contain certain subgroups that are normed vector spaces.

math.GR↗

arXiv2008

Large scale geometry of commutator subgroups

Let G be a finitely presented group, and G' its commutator subgroup. Let C be the Cayley graph of G' with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsion-free nonelementary word-hyperbolic group, C is one-ended. Hence (in this case), the asymptotic dimension of C is at least 2.

math.GR↗

arXiv2007

Irrational Stable Commutator Length in Finitely Presented Groups

We give examples of finitely presented groups containing elements with irrational (in fact, transcendental) stable commutator length, thus answering in the negative a question of M. Gromov. Our examples come from 1-dimensional dynamics, and are related to the generalized Thompson groups studied by M. Stein, I. Liousse and others.

math.GT↗