A generalized π2-diffeomorphism finiteness theorem  

作　　者：Xiaochun RONG Xuchao YAO 

机构地区：[1]Department of Mathematics,Rutgers University,New Brunswick,NJ 08903 USA [2]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Frontiers of Mathematics in China》2020年第2期399-418,共20页中国高等学校学术文摘·数学（英文）

摘　　要：Theπ2-diffeomorphism finiteness result of F.Fang-X.Rong and A.Petrunin-W.Tuschmann(independently)asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bounded above in terms of n,and upper bounds on the absolute value of sectional curvature and diameter of M.In this paper,we will generalize thisπ2-diffeomorphism finiteness by removing the condition thatπ1(M)-0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M.

关 键 词：Collapsing with bounded sectional curvature diffeomorphism finiteness vanishing second homotopy group 

分 类 号：O15[理学—数学]