Related papers: Homological stability for classical groups

The homology groups of the automorphism group of a free group are known to stabilize as the number of generators of the free group goes to infinity, and this paper relativizes this result to a family of groups that can be defined in terms…

Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…

The spectrum $\omega(G)$ of a finite group $G$ is the set of element orders of $G$. Finite groups $G$ and $H$ are isospectral if their spectra coincide. Suppose that $L$ is a simple classical group of sufficiently large dimension (the lower…

We show how to formulate some recent results from homological stability of algebras in Graham and Lehrer's language of cellular algebras. The aim is to begin to connect the new results from topology to well-established representation…

Let $G$ be a finite group. Let $U_1,U_2,\dots$ be a sequence of orthogonal representations in which any irreducible representation of $\oplus_{n \geq 1} U_n$ has infinite multiplicity. Let $V_n=\oplus_{i=1}^n U_n$ and $S(V_n)$ denote the…

We consider quotients of complete flag manifolds in Cn and Rn by an action of the symmetric group on n objects. We compute their cohomology with field coefficients of any characteristic. Specifically, we show that these topological spaces…

We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture…

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…

Let $X$ be a complex smooth quasi-projective variety with a fixed epimorphism $\nu\colon\pi_1(X)\twoheadrightarrow H$, where $H$ is a finitely generated abelian group with $\mathrm{rank}H\geq 1$. In this paper, we study the asymptotic…

We investigate homological stability for the space of sections of Fano fibrations over curves in the context of weak approximation, and establish it for projective bundles, as well as for conic and quadric surface bundles over curves.

We prove twisted homological stability for handlebody mapping class groups. Using the categorical framework developed by Randal-Williams and Wahl, we establish that the homology of the handlebody groups stabilises with respect to both genus…

We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in…

We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…

In a previous paper, the author (together with Matthew Emerton) proved that the completed cohomology groups of SL_N(Z) are stable in fixed degree as N goes to infinity (Z may be replaced by the ring O_F of integers of any number field). In…

Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect to the operator norm.

We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…

In this paper we prove that whenever $G$ is hyperbolic relative to a family of exact, ressidually finite subgroups $\{H_1, \ldots, H_n\}$, the corresponding von Neumann algebra $\mathcal L(G)$ is solid relative to the family of subalgebras…

An analog of the Tits building is defined and studied for commutative rings. We prove a Solomon-Tits theorem when $R$ either satisfies a stable range condition, or is the ring of $S$-integers of a global field. We then define an analog of…

We show that a large family of groups is uniformly stable relative to unitary groups equipped with submultiplicative norms, such as the operator, Frobenius, and Schatten $p$-norms. These include lamplighters $\Gamma \wr \Lambda$ where…

We apply our previous work on the relation between groupoid homology and K-theory to Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale space with totally disconnected stable sets, and prove that the…