2019 Algebra Topology Mini-Workshop





9:00-9:50 赵浩 (华南师范大学)

题目:Homotopy Properties of Selick's Filtration on the Double Suspension $E^2$

10:00-10:50 钟立楠 (延边大学)

题目:Computation of the Stable Homotopy Groups of Spheres

11:00-11:50 范飞飞 (中山大学)

题目:The Integral Cohomology of Real Toric Manifold

15:30-16:20 王向军 (南开大学)

题目:Some Higher Differentials in the Classical ASS

16:30-17:20 刘秀贵 (南开大学)

题目:Rational Homotopy of the Homotopy Fixed Point Sets of Lie Groups Actions


(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.