Related papers: On the cohomology ring of chains in $R^d$
We define bounded cohomology of $t$-discrete measured groupoids with coefficients into measurable bundles of Banach spaces. Our approach via homological algebra extends the classic theory developed by Ivanov and by Monod. As a consequence,…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.
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.
Let M be a moduli space of stable sheaves on a K3 or Abelian surface S. We express the class of the diagonal in the cartesian square of M in terms of the Chern classes of a universal sheaf. Consequently, we obtain generators of the…
A gauge group is the topological group of automorphisms of a principal bundle. We compute the integral cohomology ring of the classifying spaces of gauge groups of principal U(n)-bundles over the 2-sphere by generalizing the operation for…
In this paper we give the classification of rank 3 vector bundles without "inner" cohomology on a quadric hypersurface \Q_n (n>3) by studying the associated monads.
In this note we prove that the integer cohomology ring of polyhedral products with space pairs $(D^1, S^0)$ can also be described explicitly by a multiplicative Hochster's formula.
The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and…
The mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2 is determined.
We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.
Let $\MS_g$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree over a smooth complex projective curve of genus $g$. This paper proves various properties of the rational cohomology ring…
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…
De Rham cohomology, $d_V$- and $d_H$-cohomology of the differential algebra of locally pull-back exterior forms on the infinite-order jet manifold of a smooth fibre bundle are calculated.
Based on the computation of the third author we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world. Actually we obtain two such interpretations…
We show that the notion of ribbon rational homology cobordism yields a partial order on the set of aspherical $3$-manifolds, thus supporting a conjecture formulated by Daemi, Lidman, Vela-Vick and Wong. Our proof is built on Agol's recent…
Using an equivariant surgery classification, we compute the $RO(C_3)$-graded Bredon cohomology of all $C_3$-surfaces in constant $\mathbb{Z}/3$-coefficients as modules over the cohomology of a fixed point. We show that the cohomology of a…
We give a construction of the moduli space of stable maps to the classifying stack B\mu_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of \mu_r-eigenspaces of…
In this paper, we compute the cohomology ring of all homology split polyhedral product spaces and the cohomology algebra over a field of all polyhedral product spaces. As an application, we give two polyhedral product spaces such that all…
In this work we compute the Chen--Ruan cohomology and the stringy Chow ring of the moduli spaces of smooth and stable $n$-pointed curves of genus 1. We suggest a definition for an Orbifold Tautological Ring in genus 1, which is both a…
We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3-spheres up to rational homology…