Related papers: Borel's stable range for the cohomology of arithme…

The cohomology of the pure string motion group PSigma_n admits a natural action by the hyperoctahedral group W_n. Church and Farb conjectured that for each k > 0, the sequence of degree k rational cohomology groups of PSigma_n is uniformly…

We prove that in a stable range, the rational cohomology of the moduli space of curves with level structures is the same as that of the ordinary moduli space of curves.

We develop the theory of Weyl group multiple Dirichlet series for root systems of type C. For an arbitrary root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and…

Let A_2 be the moduli stack of principally polarized abelian surfaces and V a smooth l-adic sheaf on A_2 associated to an irreducible rational finite dimensional representation of Sp(4). We give an explicit expression for the cohomology of…

We prove that the completed cohomology groups of SL_N(Z) in fixed degree stabilize as N goes to infinity. We also prove that the action of Hecke operators on stable cohomology is trivial, in a precisely defined sense.

Permutative automorphisms of the Cuntz algebras $\mathcal{O}_n$ are in bijection with the stable permutations of $[n]^t$. They are also the elements of the reduced Weyl group of $Aut(\mathcal{O}_n)$. In this paper, we characterize the…

We describe additive (unstable) operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^*. We prove that there is 1-to-1 correspondence between the set…

We extend the notions of topological stability, shadowing and persistence from homeomorphisms to finitely generated group actions on uniform spaces and prove that an expansive action with either shadowing or persistence is topologically…

In this article we determine the stable cohomology groups H^i_s (A_n, Z/p) of the alternating groups A_n for all integers n and i, and all primes p.

We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…

A scheme theoretic version of the automorphism group of a grading on an algebra is presented, and the classical result that shows that, over algebraically closed fields of characteristic 0, the automorphism group of a grading is the…

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

In this mostly expository paper we review several known results about the cohomology of moduli spaces of smooth and stable curves, focusing in particular on low degree cohomology. We also give a new proof of Harer's theorem describing the…

I construct the real counterparts (which I call Borel-Bott classes) of the R/Z classes constructed in "Characteristic classes in symplectic topology", to appear, in the cohomology of volume-preserving and symplectomorhisms of a compact…

We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's…

Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…

Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and…

Let $1<p\le4$ when $n=1$ and $1<p< 3+\frac{1}{n-1} $ when $n\ge2$. We obtain the second-order horizontal Sobolev $HW^{2,2}_{\rm loc} $-regularity of $p$-harmonic functions in the Heisenberg group $\mathbb H^n$. This improves the known range…

There is a natural probability measure on the set of isomorphism classes of principally polarized Abelian varieties of dimension $g$ over $\mathbb{F}_q$, weighted by the number of automorphisms. The distributions of the number of…

We compute the rational Borel equivariant cohomology ring of a cohomogeneity-one action of a compact Lie group.