Related papers: Homological stability for unordered configuration …

Wahl recently proved that the homology of the non-orientable mapping class group stabilizes as the genus increases. In this short note we analyse the situation where the underlying non-orientable surfaces have marked points.

We show that the homology over a field of the space of free maps from the n-sphere to the n-fold suspension of X depends only on the cohomology algebra of X and compute it explicitly. We compute also the homology of the closely related…

Let $V_1, V_2, V_3, \dots $ be a sequence of $\mathbb{Q}$-vector spaces where $V_n$ carries an action of $\mathfrak{S}_n$ for each $n$. {\em Representation stability} and {\em multiplicity stability} are two related notions of when the…

Let $M$ be a simply connected closed manifold of dimension $n$. We study the rational homotopy type of the configuration space of 2 points in $M$, $F(M,2)$. When $M$ is even dimensional, we prove that the rational homotopy type of $F(M,2)$…

In this paper homology stability for unitary groups over a ring with finite unitary stable rank is established. Homology stability of symplectic groups and orthogonal groups appears as a special case of our results.

We prove that homological stability fails for the moduli space of any simply-connected closed smooth 4-manifold in any degree of homology, unlike what happens in all dimensions $\neq 4$. We detect also the homological discrepancy between…

In this note we study the homology of configuration spaces of closed manifolds. We sharpen the eventual periodicity results of Nagpal and Cantero-Palmer, prove integral homological stability for configuration spaces of odd-dimensional…

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…

We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold $(M^n,g)$ of dimension $n>2$ to any closed, non-aspherical manifold $N$ containing no stable minimal two-spheres. In particular,…

In this paper we study stability patterns in the homology of the ordered configuration space of the once-punctured torus. In the last decade Church and Church-Ellenberg-Farb proved that the homology groups of the ordered configuration space…

We prove a homotopy invariance result for a certain covering space of the space of ordered configurations of two points in $M \times X$ where $M$ is a closed smooth manifold and $X$ is any fixed aspherical space which is not a point.

We prove packing stability for any closed symplectic manifold with rational cohomology class. This will rely on a general symplectic embedding result for ellipsoids which assumes only that there is no volume obstruction and that the domain…

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…

Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…

Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold $M$, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology…

Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, homological stability…

In this paper we study the topology of the space of Riemann surfaces in a simply connected space X, S_{g,n} (X, \gamma). This is the space consisting of triples, (F_{g,n}, \phi, f), where F_{g,n} is a Riemann surface of genus g and…

Let M_g^n be the moduli space of Riemann surfaces of genus g with n labeled marked points. We prove that, for g \geq 2, the cohomology groups {H^i(M_g^n;Q)}_{n=1}^{\infty} form a sequence of Sn representations which is representation stable…

Let $M$ be a compact Riemannian manifold, and let $G$ be a compact simple Lie group with bi-invariant metric that is not $\operatorname{Sp}(n)$ for $n \geq 8$, $E_{8}$, $F_{4}$, or $G_{2}$. We show that the singular set of any stable…

We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…