# Huijun YangHenan University · Department of Mathematics

Huijun Yang

PhD

## About

13

Publications

620

Reads

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24

Citations

Citations since 2016

Introduction

**Skills and Expertise**

Additional affiliations

July 2012 - present

## Publications

Publications (13)

In this paper, complex vector bundles of rank r over 8-dimensional spinc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{c}$$\end{document} manifolds are classified in...

We define a turning of a rank-$2k$ vector bundle $E \to B$ to be a homotopy of bundle automorphisms $\psi_t$ from $\mathbb{Id}_E$, the identity of $E$, to $-\mathbb{Id}_E$, minus the identity, and call a pair $(E, \psi_t)$ a turned bundle. We investigate when vector bundles admit turnings and develop the theory of turnings and their obstructions. I...

We give necessary and sufficient conditions for a closed orientable 9-manifold M to admit an almost contact structure. The conditions are stated in terms of the Stiefel-Whitney classes of M and other more subtle homotopy invariants of M. By a fundamental result of Borman, Eliashberg and Murphy, M admits an almost contact structure if and only if M...

In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an application, we got that two rank $3$ complex vector bundles over $4$-dimensional complex projective spaces $\C P...

In this paper, the existence of almost complex structures on connected sums of almost complex manifolds and complex projective spaces are investigated. Firstly, we show that if M is a 2n-dimensional almost complex manifold, then so is \(M\sharp \overline{{\mathbb {C}}P^{n}}\), where \(\overline{{\mathbb {C}}P^{n}}\) is the n-dimensional complex pro...

Let M be an 8-dimensional closed oriented smooth manifold, ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document} be an 8-dimensional real vector bundle...

In this paper, firstly, for some $4n$-dimensional almost complex manifolds $M_{i}, ~1\le i \le \alpha$, we prove that $\left(\sharp_{i=1}^{\alpha} M_{i}\right) \sharp (\alpha{-}1) \mathbb{C} P^{2n}$ must admits an almost complex structure, where $\alpha$ is a positive integer. Secondly, for a $2n$-dimensional almost complex manifold $M$, we get tha...

Let $M$ be a $10$-dimensional closed oriented smooth manifold with $H_{1}(M;\Z)=0$ and no $2$-torsions in $H_{2}(M;\Z)$.
Then the necessary and sufficient conditions for $M$ to admit a stable almost complex structure are determined in terms of the characteristic classes and cohomology ring of $M$

Let $M$ be a $10$-dimensional closed oriented smooth manifold with $H_{1}(M;\mathbb{Z})=0$ and no $2$-torsions in $H_{2}(M;\mathbb{Z})$. Then the necessary and sufficient conditions for $M$ to admit a stable almost complex structure are determined in terms of the characteristic classes and cohomology ring of $M$.

Let (Formula presented.) be an (Formula presented.)-dimensional closed oriented smooth manifold with (Formula presented.), and (Formula presented.) be a complex vector bundle over (Formula presented.). We determine the final obstruction for (Formula presented.) to admit a stable real form in terms of the characteristic classes of (Formula presented...

Let $X$ be an $(8k+i)$-dimensional pathwise connected $CW$-complex with $i=1$ or $2$ and $k\ge0$, $\xi$ be a real vector bundle over $X$. Suppose that $\xi$ admits a stable complex structure over the $8k$-skeleton of $X$. Then we get that $\xi$ admits a stable complex structure over $X$ if the Steenrod square $$\mathrm{Sq}^{2}\colon H^{8k-1}(X;\mat...

Let M be an n-dimensional closed oriented smooth manifold with n equivalent to 0 mod 8, xi be a real vector bundle over M. Suppose that xi admits a stable complex structure over the (n 1)-skeleton of M. Then the necessary and sufficient conditions for xi to admit a stable complex structure over M are given in terms of the characteristic classes of...

Let M be a closed (n-1)-connected 2n-dimensional smooth manifold with n > 2.
In terms of the system of invariants for such manifolds introduced by Wall, we
obtain necessary and sufficient conditions for M to admit an almost complex
structure.

## Projects

Project (1)

To determine the necessary and sufficient conditions for the existence of almost complex structures on manifolds.