Related papers: Moment Angle Complexes and Big Cohen-Macaulayness

We show that for any compact connected group G the second cohomology group defined by unitary invariant 2-cocycles on \hat G is canonically isomorphic to H^2(\hat{Z(G)};T). This implies that the group of autoequivalences of the C*-tensor…

If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph $\mG_M$ with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance,…

A simple polytope $P$ is called $B$-rigid if its combinatorial type is determined by the cohomology ring of the moment-angle manifold $\mathcal{Z}_P$ over $P$. We show that any tensor product decomposition of this cohomology ring is…

For a field $\mathbb{F}$ and a triangulated compact $\mathbb{F}$-orientable manifold, consider the homology of the associated Moment-Angle ccomplex $H_*(\mathcal{Z}_{\mathcal{K}})$. We show the total homology rank…

We generalize the notion of moment-angle manifold over a simple convex polytope to an arbitrary nice manifold with corners. For a nice manifold with corners Q, we first compute the stable decomposition of the moment-angle manifold Z_Q via a…

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus.…

Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $\Sigma_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover,…

We show that when a torus $T$ acts on a smooth variety $X$, the twisted HKR isomorphism is equivariant. The main consequence is that the Bezrukavnikov- Lachowska isomorphism, relating the Hochschild cohomology of the principal block of the…

Let $T$ be a compact torus and $X$ be a a finite $T$-CW complex (e.g. a compact $T$-manifold). In earlier work, the second author introduced a functor which assigns to $X$ a so called GKM-sheaf $\mathcal{F}_X$ whose ring of global sections…

We use the Taylor resolution of a monomial ideal to compute the Tor algebra of the Stanley-Reisner ring of a simplicial complement of a simplicial complex.

Let G be a complex reductive group and K a maximal compact subgroup. If X is a smooth projective G-variety, with a fixed (not necessarily integral) K-invariant Kaehler form, then the K-action is Hamiltonian. Let M be the zero fiber of the…

Let a torus $T$ act smoothly on a compact smooth manifold $M$. If the rational equivariant cohomology $H^*_T(M)$ is a free $H^*_T(pt)$-module, then according to the Chang-Skjelbred Lemma, it can be determined by the $1$-skeleton consisting…

A real toric space is a topological space which admits a well-behaved $\mathbb{Z}_2^k$-action. Real moment-angle complexes and real toric varieties are typical examples of real toric spaces. A real toric space is determined by a pair of a…

Partial quotients of moment-angle complexes are topological analogues of smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring of such a partial quotient in terms of a…

A simplicial complex L on n vertices determines a subcomplex T_L of the n-torus, with fundamental group the right-angled Artin group G_L. Given an epimorphism \chi\colon G_L\to \Z, let T_L^\chi be the corresponding cover, with fundamental…

We show that the Hurewicz image in the homology of a moment-angle complex, when passed through an isomorphism with the Ext-module of the corresponding Stanley-Reisner ideal, contains the linear strand of this ideal. This recovers and…

Let $\mathcal C$ be category over a commutative ring $k$, its Hochschild-Mitchell homology and cohomology are denoted respectively $HH_*(\mathcal C)$ and $HH^*(\mathcal C).$ Let $G$ be a group acting on $\mathcal C$, and $\mathcal C[G]$ be…

We put a cochain complex structure ${CH}^*(\mathcal Z_K)$ on the cohomology of a moment-angle complex $\mathcal Z_K$ and call the resulting cohomology the double cohomology, ${HH}^*(\mathcal Z_K)$. We give three equivalent definitions for…

We introduce the category of {\it locally $k$-standard $T$-manifolds} which includes well-known classes of manifolds such as toric and quasitoric manifolds, good contact toric manifolds and moment-angle manifolds. They are smooth manifolds…

We show that for a Hamiltonian action of a compact torus $G$ on a compact, connected symplectic manifold $M$, the $G$-equivariant cohomology is determined by the residual $S^1$ action on the submanifolds of $M$ fixed by codimension-1 tori.…