Abstract
Given an L2-acyclic connected finite CW-complex, we define its universal L2-torsion in terms of the chain complex of its universal covering. It takes values in the weak Whitehead group Whw(G). We study its main properties such as homotopy invariance, sum formula, product formula and Poincare duality. Under certain assumptions, we can specify certain homomorphisms from the weak Whitehead group ...
Abstract
Given an L2-acyclic connected finite CW-complex, we define its universal L2-torsion in terms of the chain complex of its universal covering. It takes values in the weak Whitehead group Whw(G). We study its main properties such as homotopy invariance, sum formula, product formula and Poincare duality. Under certain assumptions, we can specify certain homomorphisms from the weak Whitehead group Whw(G) to abelian groups such as the real numbers or the Grothendieck group of integral polytopes, and the image of the universal L2-torsion can be identified with many invariants such as the L2-torsion, the L2-torsion function, twisted L2-Euler characteristics and, in the case of a 3-manifold, the dual Thurston norm polytope.
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