Steklov Institute of Mathematics at St.Petersburg

PREPRINT 5/2002

ON THE FUNDAMENTAL GROUP OF A COMPACT SPACE WITHOUT CONJUGATE POINTS

This preprint was accepted February 26, 2002
N.Lebedeva

ABSTRACT:
In 1986, C.~Croke and V.~Schroeder proved that the fundamental group $\Gamma$
of a compact analytic Riemannian manifold without conjugate points possesses
the following property: every abelian subgroup $\Gamma_0$ of $\Gamma$
is straight, that is, word metrics of $\Gamma$ and $\Gamma_0$
are Lipschitz equivalent on $\Gamma_0$.

In this paper we prove that the same property holds for the fundamental
group of any compact length space without conjugate points
(in particular, in the non-analytic Riemannian case).