Pengcheng Li

activity

20192026

most cited(Co)Homology Self-closeness Numbers of Simply-connected Spaces

6 citations · 8 across the 12 of their papers we have counts for

collaborators

12 papers

math.RT2026

Big categorification on towers of classical groups and wreath product groups

Xin Huang, Pengcheng Li, Yaolong Shen

We develop a uniform framework for ``big'' categorification of representation categories of towers of finite classical groups and wreath product groups. We construct actions of sym…

math.AT2023

Suspension Homotopy of $(n - 1)$ -connected $(2 n + 2)$ -dimensional Poincaré Duality Complexes

Pengcheng Li, Zhongjian Zhu

We study the homotopy decompositions of the suspension $Σ M$ of an $(n - 1)$ -connected $(2 n + 2)$ dimensional Poincaré duality complex $M$ , $n \geq 2$ . In particular, we completely deter…

math.RT2023★ 1 cited

Descent of splendid Rickard equivalences in $GL_{n} (q)$

Xin Huang, Pengcheng Li, Jiping Zhang

Let $n$ be a positive integer and $q$ a prime power. We prove that a refined version of Broué's abelian defect group conjecture holds for unipotent $ℓ$ -blocks of $GL_{n} (q)$ …

math.AT2022

Homotopy Types of Suspended $4$ -manifolds

Pengcheng Li

Given a closed, smooth, connected, orientable $4$ -manifold $M$ , whose integral homology groups can have $2$ -torsion, we determine the homotopy decomposition of the double suspensio…

math.AT2022

Self-closeness numbers of product spaces

Pengcheng Li

The self-closeness number of a CW-complex is a homotopy invariant defined by the minimal number $n$ such that every self-maps of $X$ which induces automorphisms on the first $n$ ho…

math.AT2022

Suspension Splitting and Cohomotopy Sets of Simply Connected $7$ -manifolds

Ruizhi Huang, Pengcheng Li

Let $M$ be a closed simply connected $7$ -manifold. In this paper we establish homotopy decompositions of the reduced suspension space $Σ M$ into a wedge sum of simpler spaces when l…

math.AT2022

On Modular Cohomotopy Groups

Pengcheng Li, Jianzhong Pan, Jie Wu

Let $p$ be a prime and let $π^{n} (X; Z / p^{r}) = [X, M_{n} (Z / p^{r})]$ be the set of homotopy classes of based maps from CW-complexes $X$ into the mod $p^{r}$ Moore spaces $M_n(\…

math.RT2021

The strengthened Broué abelian defect group conjecture for $SL (2, p^{n})$ and $GL (2, p^{n})$

Xin Huang, Pengcheng Li, Jiping Zhang

We show that each $p$ -block of $SL (2, p^{n})$ and $GL (2, p^{n})$ over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer corresponde…

math.RT2021

Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups

Pengcheng Li, Yanjun Liu, Jiping Zhang

In this paper we prove that Broué's abelian defect group conjecture is true for the finite odd-dimensional orthogonal groups $\SO_{2n+1}(q)$ at linear primes with $q$ odd. We first…

math.RT2021★ 1 cited

On the inductive blockwise Alperin weight condition for the unipotent blocks of finite groups of Lie type E_6

Yucong Du, Pengcheng Li, Shuyang Zhao

In this article, we consider the finite exceptional groups of Lie type $E_{6}$ and $^{2} E_{6}$ . We prove the inductive blockwise Alperin weight condition holds for unipotent $l$ -blocks o…

math.AT2020

Homotopy classification of based maps between $A_{n}^{2}$ -complexes

Pengcheng Li

Let $X, Y$ be $(n - 1)$ -connected finite pointed CW-complexes of dimension at most $n + 2$ , $n \geq 3$ . In this paper we give elementary proofs of the abelian group structure of $[X, Y]$ …

math.AT2019★ 6 cited

(Co)Homology Self-closeness Numbers of Simply-connected Spaces

Pengcheng Li

The (co)homology self-closeness number of a simply-connected based CW-complexes $X$ is the minimal number $k$ such that any self-map $f$ of $X$ inducing an automorphism of the (co)…

Big categorification on towers of classical groups and wreath product groups

Suspension Homotopy of (n−1)-connected (2n+2)-dimensional Poincaré Duality Complexes

Descent of splendid Rickard equivalences in GLn​(q)

Homotopy Types of Suspended 4-manifolds

Self-closeness numbers of product spaces

Suspension Splitting and Cohomotopy Sets of Simply Connected 7-manifolds

On Modular Cohomotopy Groups

The strengthened Broué abelian defect group conjecture for SL(2,pn) and GL(2,pn)

Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups

On the inductive blockwise Alperin weight condition for the unipotent blocks of finite groups of Lie type E_6

Homotopy classification of based maps between An2​-complexes

(Co)Homology Self-closeness Numbers of Simply-connected Spaces

Suspension Homotopy of $(n - 1)$ -connected $(2 n + 2)$ -dimensional Poincaré Duality Complexes

Descent of splendid Rickard equivalences in $GL_{n} (q)$

Homotopy Types of Suspended $4$ -manifolds

Suspension Splitting and Cohomotopy Sets of Simply Connected $7$ -manifolds

The strengthened Broué abelian defect group conjecture for $SL (2, p^{n})$ and $GL (2, p^{n})$

Homotopy classification of based maps between $A_{n}^{2}$ -complexes