CYCLE RANK OF LYAPUNOV GRAPHS AND THE GENERA OF MANIFOLDS

Citation
Rn. Cruz et Ka. Derezende, CYCLE RANK OF LYAPUNOV GRAPHS AND THE GENERA OF MANIFOLDS, Proceedings of the American Mathematical Society, 126(12), 1998, pp. 3715-3720
Citations number
7
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
ISSN journal
00029939
Volume
126
Issue
12
Year of publication
1998
Pages
3715 - 3720
Database
ISI
SICI code
0002-9939(1998)126:12<3715:CROLGA>2.0.ZU;2-D
Abstract
We show that the cycle-rank r(L) of a Lyapunov graph L on a manifold M satisfies: r(L) less than or equal to g(M), where g(M) is the genus o f M. This generalizes a theorem of Franks. We also show that given any integer r with 0 less than or equal to r less than or equal to g(M), r = r(L) for some Lyapunov graph L on M, dim M > 2.