Given a smooth closed S1-manifold M, this dissertation studies the extent to which certain numbers of the form (f* (x) · P · C) [M] are determined by the fixed-point set , where classifies the universal cover of is a polynomial in the Pontrjagin classes of M, and C is in the subalgebra of generated by . When various vanishing theorems follow, giving obstructions to certain fixed-point-free actions.; Let G be a connected semisimple compact Lie group.; If an S1-action on M extends to a G-action with each component of intersecting MG, then (P · C) [M] is shown to be calculable in terms of the topology of and the isotropy S1-representations. Under the same condition, (L (M) · C) [M] (L (M) being the the Hirzebruch L-class of M) is shown to depend only on the topology of the submanifold of M consisting of those components of with codimensions congruent to 0 mod 4.; These considerations yield some vanishing results. For example, if M admits a G-action with some element acting freely, then (f*(x) · P · C) [M] = 0.; If a nontrivial S1-action on a spin manifold M extends to a G-action with , then .
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机译:给定光滑封闭的 S italic> 1 super>-流形 M italic>,本文研究了一定数量的形式( f 斜体> *( x italic>)· P·C italic>)[ M italic>]由定点集展开▼