# Nilpotent action by an elementary amenable group and euler characteristic

• Lee, Jong-Bum (Department of Mathematics, Sogang University, Seoul 121-742) ;
• Park, Cnah-Young (Department of Mathematics, Kyungpook National University, Taegu 702-701)
• Published : 1996.05.01

#### Abstract

Let X be a finite connected CW-complex, $\Gamma = \pi_1(X)$ its fundamental group, $\tilde{X}$ its universal covering space. Then $\Gamma$ acts on $\tilde{X}$ by covering transformations and on the homology group $H_*(\tilde{X})$. In this note we establish the following vanishing result for the Euler characteristic $x(X)$ of X.