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Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Cycle rank of Lyapunov graphs and the genera of manifolds

Author(s): R. N. Cruz; K. A. de Rezende
Journal: Proc. Amer. Math. Soc. 126 (1998), 3715-3720.
MSC (1991): Primary 58F09, 58F25; Secondary 57R65
MathSciNet review: 1618654
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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 $M, \dim M > 2$.

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J. Milnor, Lectures on the $h$-cobordism theorem, Annals of Math. Studies, Princeton Univ. Press, Princeton, N.J, 1965. MR 32:8352

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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

DOI: 10.1090/S0002-9939-98-04957-0
PII: S 0002-9939(98)04957-0
Received by editor(s): January 22, 1997
Additional Notes: The second author was partially supported by Conselho Nacional de Desenvolvimento Cientí{}fico e Tecnológico under Grant 300072/90.2 and Fundação de Amparo à Pesquisa do Estado de São Paulo.
Communicated by: Linda Keen
Copyright of article: Copyright 1998, American Mathematical Society




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