拓扑研讨班

中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：蔡力 （西交利物浦大学）

题  目：On the loop spaces of certain polyhedral products

时  间：2023.06.21（星期三）下午14:30-15:30

地  点：数学院南楼N702

摘  要：A polyhedral product X of given topological spaces is a special subspace of their cartesian product, which is determined by a simplicial complex K. As a special case when K is a disjoint union of its vertices, X is a wedge sum. Moreover, every moment-angle manifold is homotopy equivalent to the homotopy fiber F of the inclusion of such a polyhedral product into the corresponding cartesian product. In this talk we show some recent progress on the homotopy and homology the loop spaces of general X and F, together with some relationships with simplicial groups and Hopf algebras.

=============================================

报告人：胡瑛 教授（內布拉斯加大学） 

题  目：Slope detections and the L-space Conjecture for toroidal 3-manifolds

时  间：2023.06.21（星期三）下午15:30-16:30

地  点： 南楼N702

摘  要： The L-space conjecture connects topological (taut foliations), analytic (Floer invariants), and algebraic (orderability of groups) properties of 3-manifolds, which has been a very popular topic in low dimensional topology. In this talk, we will introduce the notion of slope detections, and show results to demonstrate how slope detection is powerful notion to study the L-space conjecture for toroidal 3-manifolds.

This is joint work with Steve Boyer and Cameron Gordon.