Geodesic
Higher Dimensional Asymptotic Cycles
Canadian journal of mathematics, Tome 55 (2003) no. 3, pp. 636-648

Voir la notice de l'article provenant de la source Cambridge University Press

Given a $p$ -dimensional oriented foliation of an $n$ -dimensional compact manifold ${{M}^{n}}$ and a transversal invariant measure $\tau$ , Sullivan has defined an element of ${{H}_{p}}\left( {{M}^{n}},\,R \right)$ . This generalized the notion of a $\mu$ -asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure $\mu$ . In this one-dimensional case there was a natural 1–1 correspondence between transversal invariant measures $\tau$ and invariant measures $\mu$ when one had a smooth flow without stationary points.For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications.
DOI : 10.4153/CJM-2003-026-0
Mots-clés : 57R30, 57S20 
Schwartzman, Sol. Higher Dimensional Asymptotic Cycles. Canadian journal of mathematics, Tome 55 (2003) no. 3, pp. 636-648. doi: 10.4153/CJM-2003-026-0
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