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The $Delta$-twisted homology and fiber bundle structure of twisted simplicial sets

组织者

李京艳 , 吴杰 , 杨南君

演讲者

张蒙蒙

时间

2022年11月21日 15:30 至 17:00

地点

1129B

线上

Zoom 537 192 5549 (BIMSA)

摘要

In this talk, I will give a brief introduction for simplicial set theory. Then I will report our recent progress for unifying $delta$-homology, introduced by Alexander Grigor'yan, Yuri Muranov and Shing-Tung Yau, and twisted Cartesian product, introduced by Barratt, Gugenheim and Moore. We introduce $\Delta$-twisted Carlsson construction of $\Delta$-groups and simplicial groups, whose abelianization gives a twisted chain complex generalizeing the $delta$-homology, called $\Delta$-twisted homology. We show that Mayer-Vietoris sequence theorem holds for $\Delta$-twisted homology. Moreover, we introduce the concept of $\Delta$-twisted Cartesian product as a generalization of the twisted Cartesian product, and explore the fiber bundle structure. The notion of $\Delta$-twisted smash product, which is a canonical quotient of $\Delta$-twisted Cartesian product, is used for determining the homotopy type of $\Delta$-twisted Carlsson construction of simplicial groups.