Related papers: Toric manifolds over cyclohedra

We prove that if two closed, connected, regular cosymplectic manifolds have isomorphic groups of cosymplectomorphisms (as topological groups), then the underlying manifolds are diffeomorphic. The proof proceeds by characterizing the Reeb…

We show that the equivariant cohomology of any hyperpolar action of a compact and connected Lie group on a symmetric space of compact type is a Cohen-Macaulay ring. This generalizes some results previously obtained by the authors.

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

We compute the first and second homotopy groups of a class of contact toric manifolds in terms of the images of the associated moment map.

Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…

Cayley graphs are graphs on algebraic structures, typically groups or group-like structures. In this paper, we have obtained a few results on Cayley graphs on Cyclic groups, powers of cycles, Cayley graphs on some non-abelian groups, and…

We study the first homology group of the mapping class group and Torelli group with coefficients in the first rational homology group of the universal abelian cover of the surface. We prove two contrasting results: for surfaces with one…

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

We show that the Torelli group of a closed surface of genus $\ge 3$ acts nontrivially on the rational cohomology of its space of $3$-element subsets.

The paper associates Lagrangian submanifolds in symplectic toric varieties to certain tropical curves inside the convex polyhedral domains of $\R^n$ that appear as the images of the moment map of the toric varieties. We pay a particular…

In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…

Let $\varphi$ and $\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\varphi}(X)$ of $X$ relative to the action $\varphi$ we associate…

In this article we review some recent developments in heterotic compactifications. In particular we review an ``inherently toric'' description of certain sheaves, called equivariant sheaves, that has recently been discussed in the physics…

Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy…

We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine…

We provide a new construction of the topological cyclic homology $TC(C)$ of any spectrally-enriched $\infty$-category $C$, which affords a precise algebro-geometric interpretation of the cyclotomic trace map $K(X) \to TC(X)$ from algebraic…

It known from the work of Feigin-Tsygan, Weibel and Keller that the cohomology groups of a smooth complex variety X can be recovered from (roughly speaking) its derived category of coherent sheaves. In this paper we show that for a finite…

We give Leray-Borel-type descriptions for the mod-$2$ and the rational equivariant cohomology rings of the real and the oriented flag manifolds under the canonical torus or 2-torus actions.

We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…