Related papers: On the cohomology ring of chains in $R^d$

Let $X$ be a topological space. We consider certain generalized configuration spaces of points on $X$, obtained from the cartesian product $X^n$ by removing some intersections of diagonals. We give a systematic framework for studying the…

The rational cohomology ring of A_3, the moduli space of abelian 3-folds is computed. This is isomorphic to the the rational cohomology ring of the group Sp_3(Z) of 6x6 integral symplectic matrices. The main ingredients in the computation…

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by $-6$. The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic $3$-space.

The main result in this paper is that the space of all smooth links in Euclidean 3-space isotopic to the trivial link of n components has the same homotopy type as its finite-dimensional subspace consisting of configurations of n unlinked…

Some recent progress towards understanding the cohomology of moduli spaces of curves is described. Madsen and Weiss have given a proof of a generalisation of Mumford's conjecture on the stable cohomology of these moduli spaces M_g, and…

Refinements of the Yang-Mills stratifications of spaces of connections over a compact Riemann surface are investigated. The motivation for this study was the search for a complete set of relations between the standard generators for the…

We compute cohomology of the moduli space of genus three curves with level two structure and some related spaces. In particular, we determine the cohomology groups of the moduli space of plane quartics with level two structure as…

By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe,…

In this paper, we investigate the existence of free involutions on some Wall manifolds and we compute the mod 2 cohomology algebra of the correspondent orbit space.

Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective…

Let Rat_k be the space of based holomorphic maps from S^2 to itself of degree k. Let beta_k denote the Artin's braid group on k strings and let Bbeta_k be the classifying space of beta_k. Let C_k denote the space of configurations of length…

In this article, we introduce infinitesimal cohomology for rigid analytic spaces that are not necessarily smooth, with coefficients in a p-adic field or Fontaine's de Rham period ring.

We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank 3 and coprime degree on a smooth projective curve. Our approach involves identifying criteria to lift identities in (a…

We prove stability of the kernel bundle and prove that the cohomology bundle is simple for vector bundles associated to monads on $X = (\mathbb{P}^{n_1})^2\times\cdots\times(\mathbb{P}^{n_s})^2$ for an ample line bundle…

It is a long-established and heavily-used fact that the integral cohomology ring of the Deligne-Mumford moduli space of (complex) rational curves is the polynomial ring on the boundary divisors modulo the ideal generated by the obvious…

Inspired by Bhatt-Scholze, we introduce prismatic cohomology for rigid analytic spaces with l.c.i singularities, with coefficients over Fontaine's de Rham period ring.

We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.

In this paper we establish the existence of monads on Cartesian products of projective spaces. We construct vector bundles associated to monads on…

For any natural $d \ge k \ge 2$ we calculate the cohomology groups of the space of homogeneous polynomials $R^2 \to R$ of degree $d$, which do not vanish with multiplicity $\ge k$ on real lines. For $k=2$ this problem provides the simplest…

Let $M$ be the moduli space of rank 3 parabolic vector bundles over a Riemann surface with several punctures. By the Mehta-Seshadri correspondence, this is the space of rank 3 unitary representations of the fundamental group of the…