Tate cohomology of circle actions as a Heisenberg group

亚纯圆周作用的Swan-Tate上同调

Swan-Tate cohomology of meromorphic circle actions

该研究借助带自由圆周作用的流形配边提出对称性破缺的玩具模型，定义复定向E_∞环谱的Swan-Tate上同调并回顾H、K、MU情形下的λ-环结构。

关于圆等变的胞腔Tate滤子

On the circle-equivariant cellular Tate filtration

本文运用Jacob Lurie的论证，证明圆等变的胞腔Tate滤子上存在E₂-松紧幺半群结构，构造其合成变体并比较相关HKR滤子在两类同调上的表现。

Geometric Tate-Swan cohomology of equivariant spectra

We sketch a quick and dirty geometric approach to the Tate-Swan cohomology of equivariant spectra, illustrating it with conjectural applications to Atiyah-Segal $K$-theory of circle actions, and a possible geometric model for the topological cyclic homology of the sphere spectrum.

Periods for topological circle actions

The language of Harvey-Lawson currents and sparks may be useful for the study of Hopkins-Singer Wu classes in geometric topology, via equivariant Tate $K$-theory of circle actions and distributional generalizations of classical zeta functions.

The homotopy fixed points of the circle action on Hochschild homology

We show that Connes' B-operator on a cyclic differential graded k-module M is a model for the canonical circle action on the geometric realization of M. This implies that the negative cyclic homology and the periodic cyclic homology of a differential graded category can be identified with the homotopy fixed points and the Tate fixed points of the circle action on its Hochschild complex.

Heisenberg groups in algebraic topology

We study the Madsen-Tillmann spectrum $\C P^\infty_{-1}$ as a quotient of the Mahowald pro-object $\C P^{\infty}_{-\infty}$, which is closely related to the Tate cohomology of circle actions. That theory has an associated symplectic structure, whose symmetries define the Virasoro operations on the cohomology of moduli space constructed by Kontsevich and Witten.