相关论文: String cohomology groups of complex projective spa…

We study the classifying space of a twisted loop group $L_{\sigma}G$ where $G$ is a compact Lie group and $\sigma$ is an automorphism of $G$ of finite order modulo inner automorphisms. Equivalently, we study the $\sigma$-twisted adjoint…

These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…

For a torus bundle (S^1 x S^1) -> E -> S^1$, we construct a finite free resolution Z over ZG, where G is the fundamental group of the total space E, and then we compute the cohomology groups H^*(G,Z) and H^*(G,Z_p) for a prime p. We also…

The integral cohomology ring of the complement of an arrangement of linear subspaces of a finite dimensional complex projective space is determined by combinatorial data, i.e. the intersection poset and the dimension function.

We compute ku^*(K(Z/p,2)) and ku_*(K(Z/p,2)), the connective KU-cohomology and connective KU-homology groups of the mod-p Eilenberg-MacLane space K(Z/p,2), using the Adams spectral sequence. We obtain a striking interaction between…

With $G = \mathbb{Z}/p$, $p$ prime, we calculate the ordinary $G$-cohomology (with Burnside ring coefficients) of $\mathbb{C}P_G^\infty = B_G U(1)$, the complex projective space, a model for the classifying space for $G$-equivariant complex…

We compute the dimensions of $\operatorname{Ext}_G^n(V, W)$ for all irreducible $V$, $W$ lying in $r$-blocks of cyclic defect in the simple groups $\operatorname{Sz}(q)$, $\operatorname{PSU}_3(q)$ and $\operatorname{{}^2G}_2(q)$ in cross…

Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its classifying space, for $n>1$. Using the Serre spectral sequence associated to the fibration $BU_n\to BPU_n\to K(\mathbb{Z},3)$, we compute the integral cohomology…

We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

The Hilbert scheme X^{[a]} of points on a complex manifold X is a compactification of the configuration space of a-element subsets of X. The integral cohomology of X^{[a]} is more subtle than the rational cohomology. In this paper, we…

Let $p$ be an odd prime, and let $n\in \N$ be an integer. We show that the $n^{\text{th}}$ mod-$p$ cohomology of a solvable saturable pro-$p$ group is isomorphic to the $n^{\text{th}}$ mod-$p$ cohomology of its associated $\Z_p$-Lie algebra…

In this paper we compute the integral cohomology of the discrete groups SL(2,Z[1/p]), where p is any prime.

We compute the Hochschild cohomology groups $\HH^*(A)$ in case $A$ is a triangular string algebra, and show that its ring structure is trivial.

We describe the cohomology ring $H^*(J_2;\mathbb{F}_3)$ both as subring of $H^*(3^{1+2}_+;\mathbb{F}_3)$ and with an abstract presentation. We also give its Poincar\'{e} series. We use as tool a spectral sequence for the strongly closed…

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…

Let $G$ be the group $SL(2,\mathbb{R})$, $P\subset G$ be the parabolic subgroup of upper triangular matrices and $\Gamma\subset G$ be a cocompact lattice. A right action of $P$ on $\Gamma\backslash G$ defines an orbit foliation…

Let $\Sigma$ be an open Riemann surface and $Hol (\Sigma)$ be the Lie algebra of holomorphic vector fields on $\Sigma.$ We fix a projective structure (i.e. a local $SL_2(C)-$structure) on $\Sigma.$ We calculate the first group of cohomology…

For every ring R, we present a pair of model structures on the category of pro-spaces. In the first, the weak equivalences are detected by cohomology with coefficients in R. In the second, the weak equivalences are detected by cohomology…

In this paper we establish a connection between the cohomology of a modular Lie algebra and its p-envelopes. We also compute the cohomology of Zassenhaus algebras and their minimal p-envelopes with coefficients in generalized baby Verma…

We examine the cohomology and representation theory of a family of finite supergroup schemes of the form $(\mathbb G_a^-\times \mathbb G_a^-)\rtimes (\mathbb G_{a(r)}\times (\mathbb Z/p)^s)$. In particular, we show that a certain relation…