Cycle rank of Lyapunov graphs and the genera of manifolds
| Autor: | Ricardo N. Cruz, K. A. de Rezende |
|---|---|
| Rok vydání: | 1998 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 126:3715-3720 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-98-04957-0 |
| Popis: | We show that the cycle-rank r ( L ) r(L) of a Lyapunov graph L L on a manifold M M satisfies: r ( L ) ≤ g ( M ) r(L) \leq g(M) , where g ( M ) g(M) is the genus of M M . This generalizes a theorem of Franks. We also show that given any integer r r with 0 ≤ r ≤ g ( M ) 0 \leq r \leq g(M) , r = r ( L ) r = r(L) for some Lyapunov graph L L on M , dim M > 2 M, \dim M > 2 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|