从环面作用的等变上同调重构其轨道类型分层

等变切片滤过的一个分层

A stratification of the equivariant slice filtration

本研究构建了等变切片滤过的分层塔，将G-谱的切片谱序列分层为不同区域，各区域微分局域化切片谱序列确定，为理解完整等变切片谱序列提供了归纳方法。

等变同伦论中的 Quillen 分层

Quillen stratification in equivariant homotopy theory

本文在有限群等变同伦论中推广了 Quillen 分层定理，利用等变张量三角几何将其范畴化，并应用于 Borel 等变 Lubin--Tate $E$-理论，得到 Balmer 谱计算与局部化 $\otimes$-理想的上同调参数化。

Generalized Equivariant Cohomology and Stratifications

For $T$ a compact torus and $E_T^*$ a generalized $T$-equivariant cohomology theory, we provide a systematic framework for computing $E_T^*$ in the context of equivariantly stratified smooth complex projective varieties. This allows us to explicitly compute $E_T^*(X)$ as an $E_T^*(\text{pt})$-module when $X$ is a direct limit of smooth complex projective $T_{\mathbb{C}}$-varieties with finitely many $T$-fixed points and $E_T^*$ is one of $H_T^*(\cdot;\mathbb{Z})$, $K_T^*$, and $MU_T^*$. We perform this computation on the affine Grassmannian of a complex semisimple group.

A quotient criterion for syzygies in equivariant cohomology

Let X be a manifold with an action of a torus T such that all isotropy groups are connected and satisfying some other mild hypotheses. We provide a necessary and sufficient criterion for the T-equivariant cohomology of X with real coefficients to be a certain syzygy as a module over the cohomology of BT. It turns out that, possibly after blowing up the non-free part of the action, this only depends on the orbit space X/T together with its stratification by orbit type. Our criterion unifies and generalizes results of many authors about the freeness and torsion-freeness of equivariant cohomology…

Derived Mackey functors and $C_{p^n}$-equivariant cohomology

We establish a novel approach to computing $G$-equivariant cohomology for a finite group $G$, and demonstrate it in the case that $G = C_{p^n}$. For any commutative ring spectrum $R$, we prove a symmetric monoidal reconstruction theorem for genuine $G$-$R$-modules, which records them in terms of their geometric fixedpoints as well as gluing maps involving their Tate cohomologies. This reconstruction theorem follows from a symmetric monoidal stratification (in the sense of \cite{AMR-strat}); here we identify the gluing functors of this stratification in terms of Tate cohomology. Passing from ge…

单纯GKM轨形复形的整等变K-理论与配边环

Integral equivariant $K$-theory and cobordism ring of simplicial GKM orbifold complexes

本文定义了单纯GKM轨形复形，引入了可构建与可分性质，并计算了可分单纯GKM轨形复形的整等变上同调环、等变K-理论环及等变配边环。