Qiangbo Tan

activity

20102025

most citedSmall covers and the equivariant bordism classification of 2-torus manifolds

9 citations · 23 across the 14 of their papers we have counts for

collaborators

15 papers

math.DG2025

On the $D_{J}^{+}$ operator on higher-dimensional almost Kähler manifolds

Qiang Tan, Hongyu Wang, Ken Wang +1

In this paper, we introduce $D_{J}^{+}$ , a generalization of $\partial \partial ˉ$ operator on higher dimensional almost Kähler manifolds. Using the $D_{J}^{+}$ oper…

math.DG2023

The Calabi-Yau Equation on Symplectic Manifolds

Qiang Tan, Hongyu Wang

By using the global deformation of almost complex structures which are compatible with a symplectic form off a Lebesgue measure zero subset, we construct a (measurable) Lipschitz K…

math.DG2023

$L^{2}$ -Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture

Teng Huang, Qiang Tan, Pan Zhang

In this article, we develop an $L^{2}$ -Hodge theory on complete $2 n$ -dimensional almost Kähler manifolds $(X, ω)$ . In the first part, we establish several identities for various Lap…

math.DG2020

Remarks on some compact symplectic solvmanifolds

Qiang Tan, Adriano Tomassini

We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M = Γ\ G$ of a simply-connected solvable Lie group $G$ by a lattice $Γ$ , a…

math.DG2020★ 4 cited

$L^{2}$ -hard Lefschetz complete symplectic manifolds

Teng Huang, Qiang Tan

For a complete symplectic manifold $M^{2 n}$ , we define the $L^{2}$ -hard Lefschetz property on $M^{2 n}$ . We also prove that the complete symplectic manifold $M^{2 n}$ satisfies $L^{2…

math.DG2019

Vanishing theorems on complete Riemannian manifold with a parallel $1$ -form

Teng Huang, Qiang Tan

In this article, we first consider the $L^{2}$ \textit{Morse-Novikov cohomology} on a complete Riemannian manifold $M$ equipped with a parallel $1$ -form which includes Vaisman mani…

math.DG2017

On tamed almost complex four manifolds

Qiang Tan, Hongyu Wang, Jiuru Zhou +1

This paper proves that on any tamed closed almost complex four-manifold $(M, J)$ whose dimension of $J$ -anti-invariant cohomology is equal to the self-dual second Betti number minus…

math.SG2016★ 1 cited

Symplectic Parabolicity and L^2 Symplectic Harmonic Forms

Qiang Tan, Hongyu Wang, Jiuru Zhou

In this paper, we study the symplectic cohomologies and symplectic harmonic forms which introduced by Tseng and Yau. Based on this, we get if $(M^{2 n}, ω)$ is a compact symplectic p…

math.SG2014

A note on the deformations of almost complex structures on compact four-manifolds

Qiang Tan, Hongyu Wang, Jiuru Zhou

In this paper, we calculate the dimension of the $J$ -anti-invariant cohomology subgroup $H_{J}^{-}$ on $T^{4}$ . Inspired by the concrete example, $T^{4}$ , we get that: On…

math.SG2014★ 1 cited

Primitive cohomology of degree 2 on compact symplectic manifolds

Qiang Tan, Hongyu Wang, Jiuru Zhou

In this paper, we define the generalized Lejmi's $P_{J}$ operator on a compact almost Kähler $2 n$ -manifold. We get that $J$ is $C^{\infty}$ -pure and full if $dim ker P_{J} = b^{2} - 1$ . Addit…

math.AT2014★ 5 cited

Equivariant bordism of 2-torus manifolds and unitary toric manifolds--a survey

Zhi Lü

In this paper we survey results and recent progresses on the equivariant bordism classification of 2-torus manifolds and unitary toric manifolds.

math.SG2013★ 1 cited

Symplectic Cohomology and the Stability of J-Anti-Invariant Cohomology

Qiang Tan, Hongyu Wang, Ying Zhang +1

In this paper, we investigate the relationship between J-anti-invariant cohomology of a closed symplectic 4-manifold introduced by T.-J. Li and W. Zhang and new symplectic cohomolo…

math.SG2011★ 1 cited

On cohomology of almost complex 4-manifolds

Qiang Tan, Hongyu Wang, Ying Zhang +1

Based on recent work of T. Draghici, T.-J. Li and W. Zhang, we further investigate properties of the dimension h_J of the J-anti-invariant cohomology subgroup H_J of a closed almos…

math.AT2011★ 1 cited

Equivariant Chern numbers and the number of fixed points for unitary torus manifolds

Zhi Lü, Qiangbo Tan

Let $M^{2 n}$ be a unitary torus $(2 n)$ -manifold, i.e., a $(2 n)$ -dimensional oriented stable complex connected closed $T^{n}$ -manifold having a nonempty fixed set. In this paper we sh…

math.AT2010★ 9 cited

Small covers and the equivariant bordism classification of 2-torus manifolds

Zhi Lü, Qiangbo Tan

Associated with the Davis-Januszkiewicz theory of small covers, this paper deals with the theory of 2-torus manifolds from the viewpoint of equivariant bordism. We define a differe…

On the DJ+​ operator on higher-dimensional almost Kähler manifolds

The Calabi-Yau Equation on Symplectic Manifolds

L2-Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture

Remarks on some compact symplectic solvmanifolds

L2-hard Lefschetz complete symplectic manifolds

Vanishing theorems on complete Riemannian manifold with a parallel 1-form

On tamed almost complex four manifolds

Symplectic Parabolicity and L^2 Symplectic Harmonic Forms

A note on the deformations of almost complex structures on compact four-manifolds

Primitive cohomology of degree 2 on compact symplectic manifolds

Equivariant bordism of 2-torus manifolds and unitary toric manifolds--a survey

Symplectic Cohomology and the Stability of J-Anti-Invariant Cohomology

On cohomology of almost complex 4-manifolds

Equivariant Chern numbers and the number of fixed points for unitary torus manifolds

Small covers and the equivariant bordism classification of 2-torus manifolds

On the $D_{J}^{+}$ operator on higher-dimensional almost Kähler manifolds

$L^{2}$ -Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture

$L^{2}$ -hard Lefschetz complete symplectic manifolds

Vanishing theorems on complete Riemannian manifold with a parallel $1$ -form