Related papers: The complex of words and Nakaoka stability

We prove a general stability theorem for $p$-class groups of number fields along relative cyclic extensions of degree $p^2$, which is a generalization of a finite-extension version of Fukuda's theorem by Li, Ouyang, Xu and Zhang. As an…

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 show that the rational Novikov conjecture for a group $\Gamma$ of finite homological type follows from the mod 2 acyclicity of the Higson compactifcation of an E$\Gamma$. We then show that for groups of finite asymptotic dimension the…

We give an overview of moduli stabilization in compactifications of string theory. We summarize current methods for construction and analysis of vacua with stabilized moduli, and we describe applications to cosmology and particle physics.…

A contractible simplicial complex is constructed that parametrizes different ways of representing a fixed one-dimensional homology class in a closed orientable surface by isotopy classes of systems of disjoint oriented simple closed curves.…

Homological stability for sequences of groups is often proved by studying the spectral sequence associated to the action of a typical group in the sequence on a highly-connected simplicial complex whose stabilizers are related to previous…

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 prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of distinct sums exhibited by factors of the same length is bounded…

Let G = SU(n,1), n >1 be the orientation-preserving isometry group of the complex hyperbolic space with an Iwasawa decomposition G = KAN. We prove local rigidity of a family of certain actions of a subgroup of AN on the imaginary boundary…

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in stable cohomotopy. Using stable homotopy…

We demonstrate, using the symbolic method together with p-adic and resultant methods,the existence of systems with exactly one or two generalized symmetries. Since the existence of one or two symmetries is often taken as a sure sign (or as…

We give an different proof of our result computing the stable homology of dihedral group Hurwitz spaces. This proof employs more elementary methods, instead of higher algebra.

We study the twisted Novikov homology of the complement of a complex hypersurface in general position at infinity. We give a self-contained topological proof of the vanishing (except possibly in the middle degree) of the twisted Novikov…

Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or…

The Trotter-Suzuki decomposition is an important tool for the simulation and control of physical systems. We provide evidence for the stability of the Trotter-Suzuki decomposition. We model the error in the decomposition and determine…

We use the homological perturbation lemma to give an explicit proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.

We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…

Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of…

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…