Non-negative Ricci curvature, stability at infinity, and finite generation of fundamental groups
太阳成集团tyc411(中国)有限公司-百度百科九十周年院庆系列活动之四十八
Title: Non-negative Ricci curvature, stability at infinity, and finite generation of fundamental groups
Speaker: Jiayin Pan (UCSB)
Time: 10:30am―11:30am, July 2, 2018
Location: Lecture Hall, 4th Floor,Sir Shaw Run Run Business Administration building,School of Mathematical Sciences, Yuquan Campus
Abstract:In 1968, Milnor conjectured that any open n-manifold M of non-negative Ricci curvature has a finitely generated fundamental group. This conjecture remains open today. In this talk, we show that if there is an integer k such that any tangent cone at infinity of the Riemannian universal cover of M is a metric cone, whose maximal Euclidean factor has dimension k, then /pi_1(M) is finitely generated. In particular, this confirms the Milnor conjecture for a manifold whose universal cover has Euclidean volume growth and unique tangent cone at infinity.
Contact Person: Wenshuai Jiang (wsjiang@zju.edu.cn)