Related papers: Stability results for Houghton groups

A famous theorem of Nakaoka asserts that the cohomology of the symmetric group stabilizes. The first author generalized this theorem to non-trivial coefficient systems, in the form of $\mathrm{FI}$-modules over a field, though one now…

We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only…

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to $\#^{g}(S^{n+1}\times S^{n})$, provided $n \geq 4$. This is an odd dimensional analogue of a recent homological stability result of S. Galatius and…

We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping…

Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi…

Let C_n(M) be the configuration space of n distinct ordered points in M. We prove that if M is any connected orientable manifold (closed or open), the homology groups H_i(C_n(M); Q) are representation stable in the sense of [Church-Farb].…

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…

In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…

We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen-Hauge Dollerup and Day-Putman. We also…

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…

For a finite ring $R$, not necessarily commutative, we prove that the category of $\text{VIC}(R)$-modules over a left Noetherian ring $\mathbf{k}$ is locally Noetherian, generalizing a theorem of the authors that dealt with commutative $R$.…

We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han…

We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…

We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_\infty$-algebras, guided…

We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable…

We analyze stable homology over associative rings and obtain results over Artin algebras and commutative noetherian rings. Our study develops similarly for these classes; for simplicity we only discuss the latter here. Stable homology is a…

In this paper we study homological stability for spaces ${\rm Hom}(\mathbb{Z}^n,G)$ of pairwise commuting $n$-tuples in a Lie group $G$. We prove that for each $n\geqslant 1$, these spaces satisfy rational homological stability as $G$…

We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p - 2$. This result is…

We prove structure results for homogeneous spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function and an invariant 2-tensor. We also consider trace-free versions of these systems.…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…