Related papers: The third Milgram-Priddy class lifts

We prove that the finitely generated simple left orderable groups constructed by the second author with Hyde have vanishing second bounded cohomology, both with trivial real and trivial integral coefficients. As a consequence, these are the…

We study gradings by noncommutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if $L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$ of…

The idea that the cohomology of finite groups might be fruitfully approached via the cohomology of ambient semisimple algebraic groups was first shown to be viable in the papers [CPS75] and [CPSvdK77]. The second paper introduced, through a…

Let $p$ be an odd prime and $F$ be a number field whose $p$-class group is cyclic. Let $F_{\{\mathfrak{q}\}}$ be the maximal pro-$p$ extension of $F$ which is unramified outside a single non-$p$-adic prime ideal $\mathfrak{q}$ of $F$. In…

We prove that the cohomology ring of a finite-dimensional restricted Lie superalgebra over a field of characteristic $p > 2$ is a finitely-generated algebra. Our proof makes essential use of the explicit projective resolution of the trivial…

We prove that the Griffiths group of 3-cycles homologous to zero modulo algebraic equivalence, on a generic hypersurfaces of dimension 7 and degree 3 is not finitely generated, even when tensored with Q. Using this and a result of Nori, we…

We study a weak form of formality for differential graded algebras, called $A_3$-formality, for the cohomology of pro-p Demushkin groups at odd primes p. We show that the differential graded $\mathbb{F}_p$-algebras of continuous cochains of…

We investigate two open questions in a cohomology theory relative to the family of finite subgroups. The problem of whether the F-cohomological dimension is subadditive is reduced to extensions by groups of prime order. We show that every…

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some…

In this paper, an explicit construction of a countable parafree Lie algebra over $\mathbb Z/2$ with nonzero second homology is given. It is also shown that the cohomological dimension of the pronilpotent completion of a free noncyclic…

We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…

We show that Brin's generalisations $2V$ and $3V$ of the Thompson-Higman group $V$ are of type $FP_\infty$. Our methods also give a new proof that both groups are finitely presented.

We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal…

This paper was motivated by a question of Avner Ash, asking if it is possible to construct non-selfdual, non-monomial, cuspidal cohomology classes for suitable congruence subgroups \Gamma of SL(n,\Z). Such a construction, in special…

We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not $\forall$-homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated…

We compute the twisted cohomology of the mapping class group with level structures, with coefficients in the $r$-tensor powers of the Prym representations for any positive integer $r$. When $r\ge 2$, we show that the cohomology exhibits…

We introduce a notion of good cohomology for multiple lines in $\mathbb{P}^3$ and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that the family of space curves of degree d, not lying on a…

Let $M$ be a $G$-manifold and $\om$ a $G$-invariant exact $m$-form on $M$. We indicate when these data allow us to constract a cocycle on a group $G$ with values in the trivial $G$-module $\mathbb R$ and when this cocycle is nontrivial.

We study a closed differential form on the symmetric space of positive definite matrices, which is defined using the Pfaffian and is $\mathsf{GL}_{2n}(\mathbb{Z})$ invariant up to a sign. It gives rise to an infinite family of unstable…

Let p, ell be distinct primes and let q be a power of p. Let G be a connected compact Lie group. We show that there exists an integer b such that the mod ell cohomology of the classifying space of a finite Chevalley group G(F_q) is…