Related papers: Hirzebruch genera of manifolds with torus action

We prove that symplectic quasi-states and quasi-morphisms on a symplectic manifold descend under symplectic reduction on a superheavy level set of a Hamiltonian torus action. Using a construction due to Abreu and Macarini, in each dimension…

Consider a smooth effective action of a torus $\mathbb{T}^n$ on a connected $C^{\infty}$-manifold $M$ of dimension $m$. Then $n\leq m$. In this work we show that if $n<m$, then there exist a complete vector field $X$ on $M$ such that the…

Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.

In this paper we study a specific class of actions of a $2$-torus $\mathbb{Z}_2^k$ on manifolds, namely, the actions of complexity one in general position. We describe the orbit space of equivariantly formal $2$-torus actions of complexity…

This is a sequel of \cite{Wang}, which provides a general formalism for this paper. We mainly investigate thoroughly a subclass of toric generalized K$\ddot{a}$hler manifolds of symplectic type introduced by Boulanger in \cite{Bou}. We find…

In this article we introduce the notion of a k-almost-quasifibration and give many examples. We also show that a large class of these examples are not quasifibrations. As a consequence, supporting the Asphericity conjecture of [19], we…

We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold is Hamiltonian. In this case, we may…

Let ${\frak M}_n$ be the set of equivariant unoriented cobordism classes of all $n$-dimensional 2-torus manifolds, where an $n$-dimensional 2-torus manifold $M$ is a smooth closed manifold of dimension $n$ with effective smooth action of a…

A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence…

Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where $\frak{g}^*$ is the dual…

An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent as it is restrictive. In this article, also motivated by…

A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a K\"ahler structure if and only if it is a complex torus. We show more in general that a compact solvmanifold…

We determine conditions under which two Hamiltonian torus actions on a symplectic manifold $M$ are homotopic by a family of Hamiltonian torus actions, when $M$ is a toric manifold and when $M$ is a coadjoint orbit.

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold…

An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a…

A 2-torus manifold is a closed smooth manifold of dimension $n$ with an effective action of a 2-torus group $(\Z_2)^n$ of rank $n$, and it is said to be locally standard if it is locally isomorphic to a faithful representation of $(\Z_2)^n$…

We compute the topological simple structure set of closed manifolds which occur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an n-dimensjional torus T^n for an odd prime p and l greater or equal to 3, provided that…

Classical toric varieties are among the simplest objects in algebraic geometry. They arise in an elementary fashion as varieties parametrized by monomials whose exponents are a finite subset $\mathcal{A}$ of $\mathbb{Z}^n$. They may also be…

In the focus of our paper is a system of axioms that serves as a basis for introducing structural data for $(2n,k)$-manifolds $M^{2n}$, where $M^{2n}$ is a smooth, compact $2n$-dimensional manifold with a smooth effective action of the…

In this article, we provide an exposition about symplectic toric manifolds, which are symplectic manifolds $(M^{2n}, \omega)$ equipped with an effective Hamiltonian $\mathbb{T}^n\cong (S^1)^n$-action. We summarize the construction of $M$ as…