Cycle rank of Lyapunov graphs and the genera of manifolds
Cycle rank of Lyapunov graphs and the genera of manifolds
We show that the cycle-rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="r left-parenthesis upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>L</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">r(L)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of a Lyapunov graph <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a manifold <inline-formula content-type="math/mathml"> …