On the construction of permutation complexes for profinite groups

置换模作为CW复形同调的实现

Realization of permutation modules as homology of CW-complexes

本文研究置换模作为CW复形同调的实现问题，对任意群和特定次数的置换模给出部分解答，并完整解答了Kahn问题。

On the topology of complexes of injective words

An injective word over a finite alphabet $V$ is a sequence $w=v_1v_2\cdots v_t$ of distinct elements of $V$. The set $\mathrm{inj}(V)$ of injective words on $V$ is partially ordered by inclusion. A complex of injective words is the order complex $Δ(W)$ of a subposet $W \subset \mathrm{inj}(V)$. Complexes of injective words arose recently in applications of algebraic topology to neuroscience, and are of independent interest in topology and combinatorics. In this article we mainly study Permutation Complexes, i.e. complexes of injective words $Δ(W)$, where $W$ is the downward closed subposet of …

Koszul duality complexes for the cohomology of iterated loop spaces of spheres

The goal of this article is to make explicit a structured complex whose homology computes the cohomology of the p-profinite completion of the n-fold loop space of a sphere of dimension d=n-m<n. This complex is defined purely algebraically, in terms of characteristic structures of E_n-operads. Our construction involves: the free complete algebra in one variable associated to any E_n-operad; and an element in this free complete algebra, which is associated to a morphism from the operad of L-infinity algebras to an operadic suspension of our E_n-operad. We deduce our main theorem from: a connecti…

利用Coxeter复形对条形码空间进行分层

Stratifying the space of barcodes using Coxeter complexes

本研究运用几何群论工具，基于对称群抛物子群的带标记双陪集对含n条条带的条形码空间分层，得到推广现有不变量的新条形码不变量，并衍生出与修正瓶颈、Wasserstein度量一致的空间度量。

整系数内平凡复形的分类

The classification of integral endotrivial complexes

本文描述了交换诺特环上有限群置换模导出范畴的内平凡复形群（即皮卡群），并证明了并非所有整系数内平凡复形都来自同伦表示，同时建立了素幂阶子群的下陷结果，证明了定向内平凡复形是线丛，并给出了先驱同态的拓扑构造。