Related papers: Some computations of stable twisted homology for m…
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs, and focus on their (twisted) cohomology groups. We…
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product…
We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in…
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a…
By proving that several new complexes of embedded disks are highly connected, we obtain several new homological stability results. Our main result is homological stability for topological chiral homology on an open manifold with…
For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and…
In this paper we study the properties of Drinfeld's twisting for finite-dimensional Hopf algebras. We determine how the integral of the dual to a unimodular Hopf algebra $H$ changes under twisting of $H$. We show that the classes of…
Considering the monoidal category $\mathcal{C}$ obtained as modules over a Hopf algebra $H$ in a rigid braided category $\mathcal{B}$, we prove decomposition results for the Hochschild and cyclic homology categories $HH(\mathcal{C})$ and…
We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed…
Using the recently developed theory of finite type invariants of integral homology 3-spheres we study the structure of the Torelli group of a closed surface. Explicitly, we construct (a) natural cocycles of the Torelli group (with…
Recent work of An, Drummond-Cole, and Knudsen, as well as the author, has shown that the homology groups of configuration spaces of graphs can be equipped with the structure of a finitely generated graded module over a polynomial ring. In…
We present a formula expressing Earle's twisted 1-cocycle on the mapping class group of a closed oriented surface of genus >=2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
We construct moduli spaces of linear self-maps of projective space with marked points, up to projective equivalence. That is, we let the special linear group act simultaneously by conjugation on projective linear maps and diagonally on…
The Hilbert scheme of point modules was introduced by Artin-Tate-Van den Bergh to study non-commutative graded algebras. The key tool is the construction of a map from the algebra to a twisted ring on this Hilbert scheme. In this paper, we…
We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the first…
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 present a complete rewriting system for twisted right-angled Artin groups. Utilizing the normal form coming from the rewriting system, we provide applications that illustrate differences and similarities with right-angled Artin groups,…
Let $A$ be a cocommutative finite dimensional Hopf algebra over the field with two elements, satisfying some mild hypothesis. We set up a descent spectral sequence which computes the Picard group of the stable category of modules over $A$.…
We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct…