相关论文: The connective K-theory of the Eilenberg-MacLane s…

Tate cohomology (as well as Borel homology and cohomology) of connective K-theory for $G=(\mathbb{Z}/2)^n$ was completely calculated by Bruner and Greenlees. In this note, we essentially redo the calculation by a different, more elementary…

We develop an Eilenberg-Moore spectral sequence to compute Bredon cohomology of spaces with an action of a group given as a pullback. Using several other spectral sequences, and positive results on the Baum-Connes Conjecture, we are able to…

In this paper, we determine the connective K-cohomology with reality of elementary abelian $2$-groups as a module over $\mathbb{Z}[v_1,a]$, where $v_1$ is the equivariant Bott class and $a$ the Euler class of the sign representation. This…

Locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathcal{K}$ for a strongly self-absorbing $C^*$-algebra $D$ over a finite CW-complex $X$ form a group $E^1_D(X)$ that is the first group of a cohomology theory $E^*_D(X)$. In…

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

We announce new methods for using prismatic cohomology to compute the K-groups of $\mathbb{Z}/p^n$ and related rings. We use computer algebra methods to compute these K-groups through a large range in specific cases and also obtain explicit…

The present note presents some results about the mod-2 cohomology, modulo nilpotent elements elements of the fiber E of a decomposable map $\psi$ : K(Z, 2) $\rightarrow$ K(Z/2, p). This is more an announcement and a brief description of the…

We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope…

We compute the $\mathrm{MU}$-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n})$, of all $\mathbb{E}_1$ $\mathrm{MU}$-algebra forms of the truncated Brown--Peterson spectrum $\mathrm{BP}\langle n\rangle$. As qualitative consequences, we…

A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which…

We study the mod-2 cohomology spectral sequence arising from delooping the Bousfield-Kan cosimplicial space giving the 2-nilpotent completion of a connective spectrum $X$. Under good conditions its $E_{2}$-term is computable as certain…

KK-theory is a bivariant and homotopy-invariant functor on $C^*$-algebras that combines K-theory and K-homology. KK-groups form the morphisms in a triangulated category. Spanier-Whitehead K-Duality intertwines the homological with the…

Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…

On d\'emontre une conjecture due \'a N. Kuhn concernant la cohomologie singuli\'ere \'a coefficients mod p des espaces, comme module instable sur l'alg\'ebre de Steenrod. Notre d\'emonstration de ce r\'esultat, d\'ej\'a connu en…

Fix an odd prime $p$. Let $X$ be a pointed space whose $p$-completed K-theory $\mathrm{KU}_p^*(X)$ is an exterior algebra on a finite number of odd generators; examples include odd spheres and many H-spaces. We give a…

We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space $P(k\rho )$, of lines inside…

We study homological invariants of \'etale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology…

We study the Z/2-equivariant K-theory of the complement of the complexification of a real hyperplane arrangement. We compute the rational K and KO rings, and give two different combinatorial descriptions of the subring of the integral KO…

In this paper we introduce exotic twisted $\mathbb T$-equivariant K-theory of loop space $LZ$ depending on the (typically non-flat) holonomy line bundle ${\mathcal L}^B$ on $LZ$ induced from a gerbe with connection $B$ on $Z$. We also…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…