Related papers: Cohomological uniqueness of some $p$-groups

Let $G$ be a simply-connected, simple compact Lie group of type $\{n_{1},\ldots,n_{\ell}\}$, where $n_{1}\le\cdots \le n_{\ell}$. Let $\mathcal{G}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism…

The class of loop spaces whose mod p cohomology is Noetherian is much larger than the class of p-compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as the infinite complex…

We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested by P H…

We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show…

We study the mod p cohomology of the classifying space of the projective unitary group PU(p). We first proof that old conjectures due to J.F. Adams, and Kono and Yagita about the structure of the mod p cohomology of classifying space of…

For a fixed closed manifold $P$, we construct a cobordism category of embedded manifolds with a single Baas-Sullivan singularity of type $P$. Our main theorem identifies the homotopy type of the classifying space of this cobordism category…

We study the mod $p$ cohomology ring of the classifying space $BPU(p)$ of the projective unitary group $PU(p)$, when $p$ is an odd prime. We prove a mod $p$ formula analogous to a formula of Vistoli for the integral cohomology ring of…

We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian…

Coclass theory can be used to define infinite families of finite p-groups of a fixed coclass. It is conjectured that the groups in one of these infinite families all have isomorphic mod-p cohomology rings. Here we prove that almost all…

For a semistable family of varieties over a curve in characteristic $p$, we prove the existence of a "Clemens-Schmid type" long exact sequence for the $p$-adic cohomology. The cohomology groups appearing in such a long exact sequence are…

Let $p$ be an odd prime. Denote a Sylow $p$-subgroup of $GL_2(\mathbb{Z}/p^n)$ and $SL_2(\mathbb{Z}/p^n)$ by $S_p(n,GL)$ and $S_p(n,SL)$ respectively. The theory of stable elements tells us that the mod-$p$ cohomology of a finite group is…

We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups.

This paper defines an invariant associated to Whitehead's certain exact sequence of a simply connected CW-complex which is much more elementary - and less powerful - than the boundary invariant of Baues. Nevertheless, in good cases, it…

A finite connected CW complex which is a co-H-space is shown to have the homotopy type of a wedge of a bunch of circles and a simply-connected finite complex after almost $p$-completion at a prime $p$.

Let $X$ be a topological space with Noetherian mod $p$ cohomology and let $C^*(X;\mathbb{F}_p)$ be the commutative ring spectrum of $\mathbb{F}_p$-valued cochains on $X$. The goal of this paper is to exhibit conditions under which the…

In this paper, we define (reduced) homeology groups and (reduced) cohomeology groups on finite simpicial complexes and prove that these groups are PL homeomorphsm invariants of polyhedra, while they are not homotopy invariants. So these…

We show that the classifying space of a $p$-local compact group is approximated by a telescope of classifying spaces of $p$-local finite groups. This result has numerous implications, like a Stable Elements Theorem for $p$-local compact…

We introduce a theory of cohomological invariants with mod $p^r$ coefficients for algebraic stacks in characteristic $p$. Using these new tools we complete the computation of the Brauer group and cohomological invariants of the stack of…

In this paper we determine the rational homotopy type of the classifying space of a generic Kac-Moody group by computing its rational cohomology ring. As an application we determine the rational homology Hopf algebra of the generic…

For an arbitrary simplicial complex K, Davis and Januszkiewicz have defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of K. Subsequently, Buchstaber and Panov…