Related papers: Homology theory formulas for generalized Riemann-H…
A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…
Given a CW-complex A we define an `A-shaped' homology theory which behaves nicely towards A-homotopy groups allowing the generalization of many classical results. We also develop a relative version of the Federer spectral sequence for…
This work arose from efforts to generalise the usual cubical boundary by using different 'weights' for opposite faces, but still to obtain a chain complex, and this method was found to generalise. We describe a variant of the classical…
We study twisted cohomologies with paracompactifying families of supports. The Kunneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on these results, we eventually give explicit expressions of…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
We describe a homotopical version of the relational and gluing models of type theory, and generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy theory on inverse diagrams, and relies on the fact that Reedy…
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold M is simply connected (or more generally if the foliation is a transversely orientable Killing foliation),…
We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…
We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the…
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more…
These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…
In this paper, we construct a differential graded Lie algebra whose Maurer-Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear…
Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…
Symmetric product orbifolds provide a controlled environment to explore generic features of gauge theory and holography. The tractability of these theories lies in the complete characterisation of their gauge structure through holomorphic…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…