相关论文: Cellular cochain algebras and torus actions

For an equivariantly formal action of a compact torus $T$ on a smooth manifold $X$ with isolated fixed points we investigate the global homological properties of the graded poset $S(X)$ of face submanifolds. We prove that the condition of…

Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also…

We prove that for generalised partitions of unity ${\phi_i \mid i \in I}$ and coverings $\mathfrak{U}:={\phi_i^{-1} (R \setminus {0}) \mid i \in I}$ of a topological space $X$ the cohomology of abstract $\mathfrak{U}$-local cochains…

In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We…

We investigate the structure of circle actions with the Rokhlin property, particularly in relation to equivariant $KK$-theory. Our main results are $\mathbb{T}$-equivariant versions of celebrated results of Kirchberg: any Rokhlin action on…

We compute the cohomology rings of smooth real toric varieties and of real toric spaces, which are quotients of real moment-angle complexes by freely acting subgroups of the ambient 2-torus. The differential graded algebra we present is in…

We introduce the_inertial cohomology ring_ NH^*_T(Y) of a stably almost complex manifold carrying an action of a torus T. We show that in the case that Y has a locally free action by T, the inertial cohomology ring is isomorphic to the…

The rational Borel equivariant cohomology for actions of a compact connected Lie group is determined by restriction of the action to a maximal torus. We show that a similar reduction holds for any compact Lie group $G$ when there is a…

Let $X$ be a topological space upon which a compact connected Lie group $G$ acts. It is well-known that the equivariant cohomology $H_G^*(X;\Q)$ is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology…

We compute the structure of the cohomology ring for the quantized enveloping algebra (quantum group) $U_q$ associated to a finite-dimensional simple complex Lie algebra $\mathfrak{g}$. We show that the cohomology ring is generated as an…

Consider the space Hom(Z^n,G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of…

We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is…

We begin the systematic study of cohomological Hecke operators of modifications of coherent sheaves on a smooth surface $X$, along a fixed proper curve $Z \subset X$. We develop the necessary geometric foundations in order to define the…

We determine the $T$-equivariant integral cohomology of $F_4/T$ combinatorially by the GKM theory, where T is a maximal torus of the exceptional Lie group $F_4$ and acts on $F_4/T$ by the left multiplication.

Zonotopal algebras of vector arrangements are combinatorially-defined algebras with connections to approximation theory, introduced by Holtz and Ron and independently by Ardila and Postnikov. We show that the internal zonotopal algebra of a…

We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level…

We give a more conceptual construction of a comparison algebra morphism from the K-theoretical Hall algebra to a twist of the cohomological Hall algebra associated to a symmetric quiver, and extend the result to quivers with potential.

Let G be an exceptional Lie group with a maximal torus T. Based on Schubert calculus on the flag manifold G/T we have described the integral cohomology ring H*(G) by explicitely constructed generators in [DZ2], and determined the structure…

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…

Given an acyclic twisting cochain $\pi:C\to A$, from a curved dg coalgebra $C$ to a dg algebra $A$, we show that the associated twisted hom complex $\mathrm{Hom}^\pi_k(C,A)$ has cohomology equal to the Hochschild cohomology of $A$, as a…