Xing Gu

activity

20162024

most citedOn the Cohomology of the Classifying Spaces of Projective Unitary Groups

23 citations · 42 across the 10 of their papers we have counts for

collaborators

11 papers

math.AT2024

Topological complexity of enumerative problems and classifying spaces of $P U_{n}$

Weiyan Chen, Xing Gu

We study the topological complexity, in the sense of Smale, of three enumerative problems in algebraic geometry: finding the 27 lines on cubic surfaces, the 28 bitangents and the 2…

math.AT2023

The cohomology of $B P U (p^{m})$ and invariant polynomials

Xing Gu

Let $p$ be an odd prime. For a compact Lie group $G$ and an elementary abelian $p$ -group $A$ of $G$ , one may define the Weyl group $W_{A}$ of $A$ in a similar fashion as defining the…

math.AT2021

The $p$ -primary subgroups of the cohomology of $B P U_{n}$ in dimensions less than $2 p + 5$

Xing Gu, Yu Zhang, Zhilei Zhang +1

Let $P U_{n}$ the projective unitary group of rank $n$ and $B P U_{n}$ its classifying space. For an odd prime $p$ , we extend previous results to a compete description of $H^s(BPU_n;\math…

math.AT2021★ 1 cited

On $H^{*} (B P U_{n}; Z)$ and Weyl group invariants

Diarmuid Crowley, Xing Gu

For the projective unitary group $P U_{n}$ with a maximal torus $T_{P U_{n}}$ and Weyl group $W$ , we show that the integral restriction homomorphism \[ρ_{PU_n} \colon H^*(BPU_n;\mathbb{Z…

math.AG2020

A distinguished subring of the Chow ring and cohomology of $B P G L_{n}$

Xing Gu

We determine a subring of the Chow ring and the cohomology of $B P G L_{n}$ , the classifying space of the projective linear group of degree $n$ over complex numbers, and explain a way i…

math.AT2020★ 1 cited

On the Brown-Peterson cohomology of $B P U_{n}$ in lower dimensions and the Thom map

Xing Gu

For an odd prime $p$ , we study the image of the Thom map from Brown-Peterson cohomology of $B P U_{n}$ to the ordinary cohomology in dimensions $0 \leq i \leq 2 p + 2$ , where $B P U_{n}$ is the…

math.AT2019★ 2 cited

On The Topological Period-Index Problem over 8-manifolds

Diarmuid Crowley, Xing Gu, Christian Haesemeyer

We establish upper bounds of the indices of topological Brauer classes over a closed orientable 8-manifolds. In particular, we verify the Topological Period-Index Conjecture (TPIC)…

math.AT2019★ 1 cited

The composition of R.~Cohen's elements and the third periodic elements in stable homotopy groups of spheres

Xing Gu, Xiangjun Wang, Jianqiu Wu

In this paper, we study the cohomology of the Morava stabilizer algebra $S (3)$ . As an application, we show that for $p \geq 7$ , if $s \neq \equiv 0, \pm 1 m o d p$ , $n\not \eq…

math.AG2019★ 3 cited

Some torsion classes in the Chow ring and cohomology of $B P G L_{n}$

Xing Gu

In the integral cohomology ring of the classifying space of the projective linear group $P G L_{n}$ (over $C$ ), we find a collection of $p$ -torsions $y_{p, k}$ of degree $2(p^{…

math.AT2018★ 11 cited

The Topological Period-Index Problem over 8-Complexes, II

Xing Gu

We complete the study of the topological period-index problem over 8 dimensional finite CW complexes started in a preceding paper. More precisely, we determine the sharp upper boun…

math.AT2016★ 23 cited

On the Cohomology of the Classifying Spaces of Projective Unitary Groups

Xing Gu

Let $B P U_{n}$ be the classifying space of $P U_{n}$ , the projective unitary group of order $n$ , for $n > 1$ . We use the Serre spectral sequence associated to a fiber sequence $…

Topological complexity of enumerative problems and classifying spaces of PUn​

The cohomology of BPU(pm) and invariant polynomials

The p-primary subgroups of the cohomology of BPUn​ in dimensions less than 2p+5

On H∗(BPUn​;Z) and Weyl group invariants

A distinguished subring of the Chow ring and cohomology of BPGLn​

On the Brown-Peterson cohomology of BPUn​ in lower dimensions and the Thom map

On The Topological Period-Index Problem over 8-manifolds

The composition of R.~Cohen's elements and the third periodic elements in stable homotopy groups of spheres

Some torsion classes in the Chow ring and cohomology of BPGLn​

The Topological Period-Index Problem over 8-Complexes, II

On the Cohomology of the Classifying Spaces of Projective Unitary Groups

Topological complexity of enumerative problems and classifying spaces of $P U_{n}$

The cohomology of $B P U (p^{m})$ and invariant polynomials

The $p$ -primary subgroups of the cohomology of $B P U_{n}$ in dimensions less than $2 p + 5$

On $H^{*} (B P U_{n}; Z)$ and Weyl group invariants

A distinguished subring of the Chow ring and cohomology of $B P G L_{n}$

On the Brown-Peterson cohomology of $B P U_{n}$ in lower dimensions and the Thom map

Some torsion classes in the Chow ring and cohomology of $B P G L_{n}$