Abstract cellularization as a cellularization with respect to a set of objects

Localization with respect to a class of maps II - Equivariant cellularization and its application

We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The technique of equivariant cellularization is developed and applied to the proof of the main result.

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 $SL_3(\mathbb{R})$.

融合系统的细胞近似

Cellular approximations of fusion systems

本文研究了融合系统分类空间的细胞化问题，提出了判断分类空间是否为细胞的代数准则，并对特定异常示例进行了计算。