Welcome to the 1st 3J Topology Seminar

The 1st 3J Topology Seminar will be held at 河北正定乒乓球训练基地 from Oct. 19-20, 2019 (the 3rd weekend of October), hosted by Hebei Normal University (河北师范大学).

The seminar will be paperless. All the information about the seminar, including Talk Schedule, Abstracts of the talks, Travel Information, Accommodation and Dining arrangement, and Reimbursement Information, will be released at this page.

Message Board

Oct.12： Please note the updates in the Accommodation section
Oct.18: Please note the updates of seminar room in the Program section

Program

(Geometric and algebraic topology of manifolds）

1. All talks will take place in (综合楼5层会议室)
2. This is a 30-min talk as required by the speaker

Talks

• Yang Su (CAS)

Title: Finiteness and infiniteness of the Torelli groups of (hyper)-Kahler manifolds

Abstract: The Torelli group of a closed smooth manifold X is the subgroup of the mapping class group consisting of elements which act trivially on the integral cohomology of X. In this note we give counterexamples to a theorem by Verbitsky which states that the Torelli group of simply connected Kahler manifolds of complex dimension >2 is finite. We also give a counterexample to the theorem of Verbitsky which claims that the Torelli group of hyper-Kahler manifolds are finite. Finally we confirm the finiteness result for the special case of the hyper-Kahler manifold K[2]. This is a joint work with M.Kreck.

• Ruizhi Huang (CAS)

Title: On the topology of String manifolds of dimension $24$

Abstract: String can be viewed as higher version of Spin, while the latter plays a fundamental role in Atiyah-Singer index theory. People try to develop parallel theory for String, the whole story of which is still mystery. Geometry and topology of String manifolds then attract increasing attentions and interests. In this talk, following Hirzebruch, Mahowald-Hopkins we will discuss both the topological and index theoretical aspects of $24$-dimensional String manifolds. In particular, we will give an integral basis for the String cobordism groups at dimension 24, and also show divisibility of various characteristic classes. Besides others both the classical Borel-Hirzebruch algorithm and Duan’s Spin classes will be used for the calculations.

This is joint work with Fei Han (NUS) in progress. The initial motivation for this project is a question of Teichner, which will be also addressed and discussed. I may propose a conjecture, which is right I believe.

• Jian Liu (Nankai)

Title: On the injection of the fixed point set into the homotopy fixed point set

Abstract: Given an action of a compact connected Lie group $G$ on the rational nilpotent $G$-space $X$, there exists a natural injection $k:X^{G}\hookrightarrow X^{hG}$ of the fixed point set into the homotopy fixed set. In this topic, we make use of the inclusion $j: X^{G}\hookrightarrow X$ to give an equivalent condition for the rational homotopy morphism $\pi_{\ast}(k)\otimes \mathbb{Q}$ to be injective. Moreover, we provide a necessary and sufficient condition for the injection $k$ being a rational homotopy equivalence. Our results generalize some known results.

• Pengcheng Li (CAS)

Title: Introduction to Chang Complexes

Abstract: In this talk I shall give a brief introduction to the study of Chang complexes motivated by some classical and famous results of Moore spaces.

• 张志国 (HNU)

题目:拓扑邻接范畴下的强同伦及其推广
摘要:本报告主要介绍拓扑邻接范畴下的强同伦的背景，概念，意义，性质及其在图上的推广！

• Xiangjun Wang (Nankai)

题目:八分之十一猜想

摘要:在这个报告中我将从单连通4维流行的上同调环讲起，介绍八分之十一猜想的内容及最新进展。

Travel Information

地址：河北省石家庄市正定县兴荣路63号

乘车路线：

1. 石家庄火车站：
   方案一：乘公交车148路到大正驾校站换乘164路，至正定乒乓球训练基地（以下简称“基地”）即到；
   方案二：地铁，石家庄火车站乘3号线-新百广场乘1号线（福泽方向）-商务中心D口-乘出租车（大约10元）到基地或换乘143路公交；
   方案三：出租车，石家庄火车站到“基地”，大约80元。
2. 正定机场高铁站：乘出租车到“基地”， 大约60元。
3. 石家庄机场：乘机场巴士到金星假日酒店下车，十字路口处西行100米即到。
4. 石家庄北站：乘出租车到“基地”下车， 大约60元。
5. 自驾车：正定高速路口下，西行（即下高速左转）见肝病医院，第一个十字路口处左转南行，第一个红绿灯丁字路口右转西行约800米，丁字路口左转（隆兴寺方向）约500米处十字路口处右转沿兴荣路直行100米即到。

Nearby, there are several interesting places including: 荣国府与宁荣街，隆兴寺，赵云庙

Accommodation

1. Registration and accommodation are arranged at 公寓楼, where all the participants will stay.

2. Breakfast, Lunch and Dinner are available at 综合楼; 4楼 早午餐，1楼晚餐

(正定乒乓球基地平面示意图) You may have to use web browser to open the image instead of Wechat!

Reimbursement Information

To apply reimbursement from the host, please contact Professor Yanhong Ding (丁雁鸿老师，yanhongding@163.com) with the following:

1. 来回火车票

Mailing Address:
河北省石家庄市南二环东路20号
河北师范大学数学科学学院
丁雁鸿 13722799311