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Register a new userFarrell-Jones Conjecture for free-by-cyclic groups
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We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.
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We prove the Farrell-Jones Conjecture for mapping tori of automorphisms of virtually torsion-free hyperbolic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture by Bartels-L{u}ck-Reich, as well as the structure theory of mapping tori by Dahmani-Krishna.
We give an algorithm to compute stable commutator length in free products of cyclic groups which is polynomial time in the length of the input, the number of factors, and the orders of the finite factors. We also describe some experimental and theoretical applications of this algorithm.
Let $$1 to H to G to Q to 1$$ be an exact sequence where $H= pi_1(S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is finitely generated free. The aim of this paper is to provide sufficient conditions to prove that $G$ is cubulable and construct examples satisfying these conditions. The main result may be thought of as a combination theorem for virtually special hyperbolic groups when the amalgamating subgroup is not quasiconvex. Ingredients include the theory of tracks, the quasiconvex hierarchy theorem of Wise, the distance estimates in the mapping class group from subsurface projections due to Masur-Minsky and the model geometry for doubly degenerate Kleinian surface groups used in the proof of the ending lamination theorem.
Let $text{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g geq 1$. For $k geq 2$, we consider the standard $k$-sheeted regular cover $p_k: S_{k(g-1)+1} to S_g$, and analyze the liftable mapping class group $text{LMod}_{p_k}(S_g)$ associated with the cover $p_k$. In particular, we show that $text{LMod}_{p_k}(S_g)$ is the stabilizer subgroup of $text{Mod}(S_g)$ with respect to a collection of vectors in $H_1(S_g,mathbb{Z}_k)$, and also derive a symplectic criterion for the liftability of a given mapping class under $p_k$. As an application of this criterion, we obtain a normal series of $text{LMod}_{p_k}(S_g)$, which generalizes of a well known normal series of congruence subgroups in $text{SL}(2,mathbb{Z})$. Among other applications, we describe a procedure for obtaining a finite generating set for $text{LMod}_{p_k}(S_g)$ and examine the liftability of certain finite-order and pseudo-Anosov mapping classes.
In this paper we study smooth orientation-preserving free actions of the cyclic group $mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds, $sharp g (S^n times S^n)sharp Sigma$, where $Sigma$ is a homotopy $2n$-sphere. When $n=2$ we obtain a classification up to topological conjugation. When $n=3$ we obtain a classification up to smooth conjugation. When $n ge 4$ we obtain a classification up to smooth conjugation when the prime factors of $m$ are larger than a constant $C(n)$.
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