In this paper,we mainly consider the nonexistences of minimal distal actions by some groups on compact manifolds,particularly on surfaces.Suppose that X is a compact manifold andΓis a finitely generated group acting ...In this paper,we mainly consider the nonexistences of minimal distal actions by some groups on compact manifolds,particularly on surfaces.Suppose that X is a compact manifold andΓis a finitely generated group acting on X.We show in the following cases thatΓcannot act on X minimally and distally.(1)X is connected and the firstČech cohomology groupȞ^(1)(X)with integer coefficients is nontrivial andΓis amenable;(2)X is the 2-sphere S^(2)or the real projective plane■andΓcontains no nonabelian free subgroup;(3)X is a closed surface andΓis a lattice of SL(n,ℝ)(n≥3).展开更多
基金supported by NNSF(Grant No.12271388)supported by NNSF(Grant Nos.12201599,12371196)。
文摘In this paper,we mainly consider the nonexistences of minimal distal actions by some groups on compact manifolds,particularly on surfaces.Suppose that X is a compact manifold andΓis a finitely generated group acting on X.We show in the following cases thatΓcannot act on X minimally and distally.(1)X is connected and the firstČech cohomology groupȞ^(1)(X)with integer coefficients is nontrivial andΓis amenable;(2)X is the 2-sphere S^(2)or the real projective plane■andΓcontains no nonabelian free subgroup;(3)X is a closed surface andΓis a lattice of SL(n,ℝ)(n≥3).
