Related papers: Central stability homology
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…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
We establish a decomposition of stable homology of automorphism groups of free groups with polynomial contravariant coefficients in term of functor homology. This allows several explicit computations, intersecting results obtained by…
We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a…
Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…
We prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S^n x S^n, in the…
Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The…
We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-modules (namely the local degree and regularity, together with the stable…
In the context of holomorphic families of ${\mathbb P}^k$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the architecture of the proof of certain results of [BBD]
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…
Following the argument for diffeomorphisms by Galatius and Randal-Williams, we prove that homeomorphisms of 1-connected manifolds of even dimension at least 6 exhibit homological stability. We deduce similar results for PL homeomorphisms…
In this paper we prove homological stability for certain subgroups of surface braid groups. Alternatively, this is equivalent to proving homological stability for configurations of subsets of exactly $\xi$ points in a surface as we increase…
We introduce the notion of a polynomial stability condition, generalizing Bridgeland stability conditions on triangulated categories. We construct and study a family of polynomial stability conditions for any normal projective variety. This…
From a root system, one may consider the arrangement of reflecting hyperplanes, as well as its toric and elliptic analogues. The corresponding Weyl group acts on the complement of the arrangement and hence on its cohomology. We consider a…
We compute the rational stable homology of the automorphism groups of free nilpotent groups. These groups interpolate between the general linear groups over the ring of integers and the automorphism groups of free groups, and we employ…
We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…
We improve, by a factor of 2, known homology stability ranges for the integral homology of symplectic groups over commutative local rings with infinite residue field and show that the obstruction to further stability is bounded below by…
We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher…
We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homology by the polynomial ring generated by the set of edges,…
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…