Related papers: Twisted homological stability for handlebody mappi…
A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…
We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite…
In this paper we prove a homological stability theorem for the diffeomorphism groups of high dimensional manifolds with boundary, with respect to forming the boundary connected sum with the product $D^{p+1}\times S^{q}$ for $|q - p| <…
We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of…
We prove a new kind of stabilisation result, "secondary homological stability", for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the…
In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of…
This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C_n(M;X) of configurations of n unordered points in a connected open manifold M with labels in a…
We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and…
In [Chu12], Church used representation stability to prove that the space of configurations of distinct unordered points in a closed manifold exhibit rational homological stability. A second proof was also given by Randal-Williams in [RW11]…
We introduce a new method for proving twisted homological stability, and use it to prove such results for symmetric groups and general linear groups. In addition to sometimes slightly improving the stable range given by the traditional…
In this article, we extend an argument of Vogtmann in order to show homology stability of the Euclidean orthogonal group $O_n(A)$ when $A$ is a valuation ring subject to arithmetic conditions on either its residue or its quotient field. In…
Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
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…
We study the cohomology with twisted coefficients of the geometric realization of a linking system associated to a saturated fusion system $\mathcal{F}$. More precisely, we extend a result due to Broto, Levi and Oliver to twisted…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
We prove that homological stability holds for configuration spaces of orbifolds. This builds on the work of Bailes' thesis where he proves that the stabilisation maps are injective.
Homological stability for unordered configuration spaces of connected manifolds was discovered by Th. Church and extended by O. Randal-Williams and B. Knudsen: $H_i(C_k(M);\mathbb{Q})$ is constant for $k\geq f(i)$. We characterize the…
We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's…
We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as…