Topological obstructions to certain Lie group actions on manifolds
نویسندگان
چکیده
منابع مشابه
Topological Obstructions to Certain Lie Group Actions on Manifolds
Given a smooth closed S1-manifold M , this article studies the extent to which certain numbers of the form (f∗ (x) · P · C) [M ] are determined by the fixed-point set MS 1 , where f : M → K (π1 (M) , 1) classifies the universal cover of M , x ∈ H∗ (π1 (M) ;Q), P is a polynomial in the Pontrjagin classes of M , and C is in the subalgebra of H∗ (M ;Q) generated by H2 (M ;Q). When MS 1 = ∅, variou...
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Results are given on the integrability of certain distributions which arise from smoothly parametrized families of diffeomorphisms acting on manifolds. Applications to control problems and in particular to the problem of sampling are discussed.
متن کاملLie group actions on compact
Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03788-8