将空间几何分解为不同类型的单元

持久极小模型的胞腔分解

Cell decompositions of persistent minimal models

本文将有理同伦论结构定理推广到持久化情形，通过胞腔附着的迭代序列显式构造驯顺持久CDGA的极小模型，并给出余持久单连通空间有理Postnikov塔的显式分解。

Cellularization for exceptional spherical space forms and the flag manifold of $SL_3(\mathbb{R})$

We construct an explicit equivariant cellular decomposition of the $(4n-1)$-sphere with respect to binary polyhedral groups, and describe the associated cellular homology chain complex. As a corollary of the binary octahedral case, we deduce an $\mathfrak{S}_3$-equivariant decomposition of the flag manifold of $SL_3(\mathbb{R})$.

A cell decomposition of the Fulton MacPherson operad

We construct a small regular cellular decomposition of the Fulton MacPherson operad $FM_2$ that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti operad. We compute the generating functions counting the cells, that are algebraic.

模空间的紧化与胞腔分解

Compactifications of Moduli Spaces and Cellular Decompositions

本文研究含闭Riemann曲面的模空间的紧化。第一个主要结果确定了这些紧化的同胚类型。第二个主要结果介绍了这些空间上使用半稳定带状图扩展早期的工作Looijenga的orbicell分解。

Cell decompositions of character varieties

We establish curious Lefschetz property for generic character varieties of Riemann surfaces conjectured by Hausel, Letellier and Rodriguez-Villegas. Our main tool applies directly in the case when there is at least one puncture where the local monodromy has distinct eigenvalues. We pass to a vector bundle over the character variety, which is then decomposed into cells, which look like vector bundles over varieties associated to braids by Shende-Treumann-Zaslow. These varieties are in turn decomposed into cells that look like $(\mathbb{C}^*)^{d-2k}\times \mathbb{C}^k$. The curious Lefschetz pro…