ON THE YAGITA INVARIANT OF MAPPING CLASS GROUPS
H. H. Glover, G. Mislin and Y. Xia
March 1993

Abstract. Let $\Gamma$ denote a group of finite virtual cohomological 
dimension and $p$ a prime. If the cohomology ring $H^*(\Gamma,\mathbb F_p)$ 
has Krull dimension one, the $p$-period of $\Gamma$ is defined; it measures 
the periodicity of $H^*(\Gamma,\mathbb F_p)$ in degrees above the virtual 
cohomological dimension of $\Gamma$. The Yagita invariant $p(\Gamma)$ of 
$\Gamma$ is a natural generalization of the $p$-period to groups with
$H^*(\Gamma,\mathbb F_p)$ of Krull dimension larger than one. We compute the 
Yagita invariant $p(\Gamma_g)$ for the mapping class group $\Gamma_g$ with 
respect to an arbitrary odd regular prime $p$.