Related papers: A Cartan-Eilenberg spectral sequence for a non-nor…

If Y is a diagram of spectra indexed by an arbitrary poset C together with a specified sub-poset D, we define the total cofibre \Gamma (Y) of Y as the strict cofibre of the map from hocolim_D (Y) to hocolim_C (Y). We construct a comparison…

Let $(M,g)$ an open and oriented riemannian manifold. The aim of this paper is to study some properties of the two following sequences of $L^2$ cohomology groups: $H^i_{2,m\rightarrow M}(M,g)$ defined as the image…

We introduce and begin to analyse a class of algebras, associated to congruence subgroups, that extend both the algebra of modular forms of all levels and the ring of classical Hecke operators. At the intuitive level, these are algebras of…

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for…

For an incidence geometry $\mathcal{G} = (\mathcal{P}, \mathcal{L}, \text{I})$ with a linear representation $\mathcal{T}_n^*(\mathcal{K})$, we apply WQH switching to construct a non-geometric graph $\Gamma'$ cospectral with the line graph…

Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Suppose $\mathcal{X}_G$ has dimension $n$ and it has no factor isometric to either $\mathbb{H}^2$ or…

At the prime $2$, let $\mathcal{B}$ denote the secondary Steenrod algebra in the sense of Baues, Baues--Jibladze, Nassau, and Baues--Frankland. We determine the secondary Ext groups of the secondary cohomology objects of the three fibers…

In recent years a Hopf algebraic structure underlying the process of renormalization in quantum field theory was found. It led to a Birkhoff factorization for (regularized) Hopf algebra characters, i.e. for Feynman rules. In this work we…

For any rank-one Riemannian symmetric space S of non-compact type and any discrete, cofinite, non-cocompact, torsion-free group $\Gamma$ of orientation-preserving Riemannian isometries on S, we develop a cohomological interpretation for the…

Suppose the ground field to be algebraically closed and of characteristic different from $2$ and $3$. All Heisenberg Lie superalgebras consist of two super versions of the Heisenberg Lie algebras, $\frak{h}_{2m,n}$ and $\frak{ba}_n$ with…

We set up machinery for recognizing k-cellular modules and k-cellular approximations, where k is an R-module and R is either a ring or a ring-spectrum. Using this machinery we can identify the target of the Eilenberg-Moore cohomology…

Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of…

We are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain $\Omega\subset {\mathbb R}^d$, $d\ge 1$. We assume $\Omega$ to be Lebesgue measurable with regular boundary and contained,…

We study the Adams-Novikov spectral sequence in $\mathbb{F}_p$-synthetic spectra, computing the synthetic analogs of $\mathrm{BP}$ and its cooperations to identify the synthetic Adams-Novikov $\mathrm{E}_2$-page, computed in a range with a…

The mapping class group $\Gamma^k(N_g)$ of a non-orientable surface with punctures is studied via classical homotopy theory of configuration spaces. In particular, we obtain a non-orientable version of the Birman exact sequence. In the case…

We propose a Hodge theory for the spaces $E_2^{p,\,q}$ featuring at the second step either in the Fr\"olicher spectral sequence of an arbitrary compact complex manifold $X$ or in the spectral sequence associated with a pair $(N,\,F)$ of…

An invariant for cospectral graphs is a property shared by all cospectral graphs. In this paper, we establish three novel arithmetic invariants for cospectral graphs, revealing deep connections between spectral properties and combinatorial…

For an additive Waldhausen category linear over a ring $k$, the corresponding $K$-theory spectrum is a module spectrum over the $K$-theory spectrum of $k$. Thus if $k$ is a finite field of characteristic $p$, then after localization at $p$,…

In 1999 A. Connes and D. Kreimer have discovered a Hopf algebra structure on the Feynman graphs of scalar field theory. They have found that the renormalization can be interpreted as a solving of some Riemann - Hilbert problem. In this work…

Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of ``additive groupoid enriched categories'', in which a secondary analog of homological algebra can…