# 2019代数拓扑小型研讨会

日程表

9:00-9:50   赵浩 （华南师范大学）

10:00-10:50  钟立楠 （延边大学）

11:00-11:50 范飞飞 （中山大学）

15:30-16:20 王向军 (南开大学)

16:30-17:20 刘秀贵 (南开大学)

(赵浩) In this talk I will show how to correspondingly filter $BW_{n}$ in a manner compatible
with Selick's filtration and the fibration $$\nameddright{S^{2n-1}}{E^{2}}{\Omega^{2} S^{2n+1}}{}{BW_{n}}$$, study the multiplicative properties of the spaces in the filtrations, and use the filtrations to filter exponent information for the homotopy groups of $S^{2n+1}$.  Our results link three seemingly different in nature classical fibrations given by Toda, Selick and Gray and make them special cases of a systematic whole.

（钟立楠）One of the central problems in homotopy theory is the computation of the stable homotopy groups of spheres. The main computation tools are Adams spectral sequence and Adams-Novikov spectral sequence. This reprot will mainly consider the convergence of the product elements in the stable homotopy groups of sphere when s>p.

（范飞飞） Let   be a toric variety of complex dimension  . Then there is a canonical involution, called the conjugation of  . The set of its fixed points, denoted by  , is a real subvariety of dimension  , called a real toric variety. When   is a toric manifold, then   is a submanifold of dimension   and called a real toric manifold. In this talk we introduce a formula to calculate the integral cohomology ring of the real toric manifold   by using Cartan-Leray spectral sequence.

(王向军）In this talk I will introduce how to compute the secondary differentials in the classical Adams spectral sequence by the matrix Massey product. I will also introduce how to compute the higher Adams differentials by the Algebraic Novikov spectral sequence. At last I will introduce an Adams differential deduced from the homotopy element $\beta_{p^2/p^2-1}$.

(刘秀贵)  An action of a group $G$ on a space gives rise to two natural spaces, the fixed point set and the homotopy fixed point set. In this talk, when $G$ is $S^3$ or $S^1\times S^3$ and $M$ is a $G$-space, we study the rational homotopy type of the homotopy fixed point set $M^{hG}$, and the natural injection $M^G\rightarrow M^{hG}$. This is a joint work with Yanlong Hao, Qianwen Sun and Sang Xie.

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