Cycle rank of Lyapunov graphs and the genera of manifolds-Reference-Cited by-同舟云学术

Cycle rank of Lyapunov graphs and the genera of manifolds

Published:1998 Issue:12 Volume:126 Page:3715-3720
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Cruz R.,de Rezende K.

Abstract

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 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1998-126-12/S0002-9939-98-04957-0/S0002-9939-98-04957-0.pdf

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