$L^2$-torsion of fibrations

Abstract

The paper studies the $L^2$-torsion of fibrations, focusing on cases that relax acyclicity and the determinant class condition. We prove the sum formula and the product formula for $L^2$-torsion in the extended abelian category. The desired formula for $L^2$-torsion of a simple fibration is obtained under the assumption that the fibers have zero Euler characteristic.