Related papers: Loop space homology associated to the mod 2 Dickso…

We show that the mod 2 Seiberg-Witten invariant can be determined for a spin manifold X which has the same homology groups as the 4-torus. The value depends on the structure of the cohomology ring of X, and in particular on the 4-fold cup…

Carlsson's construction is a simplicial group whose geometric realization is the loop space of the 1-stunted reduced Borel construction. Our main results are: i) Given a pointed simplicial set acted upon by the discrete cyclic group C_2 of…

In this paper, we calculate $RO(C_2)$-graded cohomology of $C_2$-equivariant Eilenberg-Mac Lane spaces $K(\underline{Z/2}, n+\sigma)$ for $n\geq 0$. These can be used to give the relation between equivariant lambda algebra and equivariant…

We calculate mod-p cohomology of extended powers, and their group completions which are free infinite loop spaces. We consider the cohomology of all extended powers of a space together and identify a Hopf ring structure with divided powers…

The main result of this paper is an application of the topology of the space $Q(X)$ to obtain results for the cohomology of the symmetric group on $d$ letters, $\Sigma_d$, with `twisted' coefficients in various choices of Young modules and…

A spectral sequence for the computation of the Hochschild cohomology of a coconnective dga over a field is presented. This spectral sequence has a similar flavour to the spectral sequence constructed by Cohen, Jones and Yan for the…

For an arrangement with complement X and fundamental group G, we relate the truncated cohomology ring, H^{<=2}(X), to the second nilpotent quotient, G/G_3. We define invariants of G/G_3 by counting normal subgroups of a fixed prime index p,…

We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8…

Dwyer, Miller and Wilkerson proved that at the prime 2, the classifying spaces of SU(2) and SO(3) can be obtained as a homotopy pushout of the classifying spaces of certain subgroups. In this paper we show explicitly how these…

Let p be an odd prime. Let G be a p-local finite group over the extraspecial p-group p_+^{1+2}. In this paper we study the cohomology and the stable splitting of their p-complete classifying space BG.

We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…

We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring $C_q[SL_2]$ at odd roots of unity and with its standard 4-dimensional differential structure. We find that $H^1$ and $H^3$ have three…

We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures…

We will determine the motivic cohomology $H^{*,*}(BSO_n , Z/2)$ with coefficients in $Z/ 2$ of the classifying space of special orthogonal groups $SO_n$ over the complex numbers $C$.

We extend the computations in [AGM4] to find the mod 2 homology in degree 1 of a congruence subgroup Gamma of SL(4,Z) with coefficients in the sharbly complex, along with the action of the Hecke algebra. This homology group is closely…

Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary forms of degree $d$--labelled by partitions of $d$. Given a partition $\lambda$, let $X_\lambda$ be the set of forms with root multiplicity corresponding to $\lambda$.…

N Kuhn has given several conjectures on the special features satisfied by the singular cohomology of topological spaces with coefficients in a finite prime field, as modules over the Steenrod algebra. The so-called realization conjecture…

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…

We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…

In this paper we consider classifying spaces of a family of $p$-groups and we prove that mod $p$ cohomology enriched with Bockstein spectral sequences determines their homotopy type among $p$-completed CW-complexes. We end with some…