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Bounding Topology via Geometry,A-Simple Fundamental Groups
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作者 Xiaochun Rong xuchao yao 《Communications in Mathematical Research》 CSCD 2020年第4期489-505,共17页
We call a group A-simple,if it has no non-trivial normal abelian subgroup.We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are A-simple.
关键词 A-simple fundamental group collapsing with bounded sectional curvature finiteness of fundamental groups and diffeomorphic types.
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A generalized π2-diffeomorphism finiteness theorem 被引量:1
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作者 Xiaochun RONG xuchao yao 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第2期399-418,共20页
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 bo... 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. 展开更多
关键词 Collapsing with bounded sectional curvature diffeomorphism finiteness vanishing second homotopy group
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