ASYMPTOTIC CYCLES FOR ACTIONS OF LIE GROUPS

作者：Schwartzman Sol^*

来源：Proceedings of the American Mathematical Society, 2013, 141(5): 1673-1677.

Let M-k be a compact C-infinity manifold and suppose we are given a C-infinity action of R-n on M-k. If p is a quasiregular point for this action and v is an r-vector over the Lie algebra of Rn, we show how to associate with p and v an element A(p)(v) in H-r(M-k; R). When n = 1 and v is the usual generator for the Lie algebra of R, A(p)(v) coincides with the asymptotic cycle associated with p by our flow. Just as in the one dimensional case, with any invariant probability measure we can associate an element A(mu)(v) in Hr(M-k; R). %26lt;br%26gt;Several results known in the one dimensional case generalize to our present situation. The results we have stated for actions of Rn are obtained from a discussion of what we can say when we have a smooth action of an arbitrary connected Lie group on M-k.

• 出版日期2013-5