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【韩国仁荷大学】An infinite family of nongeometric embeddings of braid group into MCG and their homology triviality

2019年05月29日 08:57  点击:[]

报告题目: An infinite family of nongeometric embeddings of braid group into MCG and their homology triviality

 

报告人: Yongjin Song  教授(韩国仁荷大学)

 

报告校内联系人:雷逢春    联系方式:84708360

 

报告时间:  201966日(星期四) 15:00-16:30

 

报告地点: 创新园大厦A1101

 

报告摘要The 3-fold branched coverings over a disk with some branch points induce a new nongeometric embedding of braid groups into mapping class groups. Each generator of braid group is mapped  to a kind of 1/6 rotation on some part of the surface which  turns out to be a product of two Dehn twists. We may consider more general case; n-fold covering for n>3.  The n-fold branched  coverings over a disk induce a nongeometric embedding in a similar way to the case of 3-fold covering. In the case of n-fold covering, the induced embedding maps each generator of braid group to a product of n-1 Dehn twists along n-1 consecutive closed curves. We prove that all these new embeddings induce trivial homology homomorphism for any coefficient. We prove this by showing that these embeddings preserve the little 2-cube operad action on the configuration spaces and on the moduli spaces.

 

报告人简介: Yongjin SONG,韩国仁荷大学数学系教授, 现任韩国数学会副理事长,韩国数学会奥数委员会主任,韩国数学奥林匹克队顾问,主要从事代数拓扑领域中的范畴论、同伦论、环路空间结构、辫子群、映射类群和Artin群等方面的研究工作,是代数拓扑领域国际知名专家,2010年曾获韩国数学会最佳指导论文奖(相当于国内的博士百优论文奖),多次承担韩国国家研究基金项目,多次组织主办学术会议,包括韩国大宇纯数学研讨会、日韩代数拓扑会议、中日韩代数拓扑会议、东亚代数拓扑会议、国际数学家大会代数拓扑卫星会议、韩国数学会拓扑研讨会等。

 

 

数学科学学院

2019529

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