Cycle rank of Lyapunov graphs and the genera of manifolds
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- by R. N. Cruz and K. A. de Rezende PDF
- Proc. Amer. Math. Soc. 126 (1998), 3715-3720 Request permission
Abstract:
We show that the cycle-rank $r(L)$ of a Lyapunov graph $L$ on a manifold $M$ satisfies: $r(L) \leq g(M)$, where $g(M)$ is the genus of $M$. This generalizes a theorem of Franks. We also show that given any integer $r$ with $0 \leq r \leq g(M)$, $r = r(L)$ for some Lyapunov graph $L$ on $M, \dim M > 2$.References
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Additional Information
- R. N. Cruz
- Affiliation: Departamento de Matemática Universidade Estadual de Campinas 13083-970 Campinas, São Paulo, Brazil
- Email: cruz@turing.unicamp.br
- K. A. de Rezende
- Affiliation: Departamento de Matemática Universidade Estadual de Campinas 13083-970 Campinas, São Paulo, Brazil
- Email: ketty@ime.unicamp.br
- Received by editor(s): January 22, 1997
- Additional Notes: The second author was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico under Grant 300072/90.2 and Fundação de Amparo à Pesquisa do Estado de São Paulo.
- Communicated by: Linda Keen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3715-3720
- MSC (1991): Primary 58F09, 58F25; Secondary 57R65
- DOI: https://doi.org/10.1090/S0002-9939-98-04957-0
- MathSciNet review: 1618654