The Klein-Williams invariant is functorial; for simply-connected spaces the universal invariant group is the free abelian group on irreducible characteristic polynomials; and ℓ_G and λ_G vanish simultaneously.
Dold,Fixed point index and fixed point theorem for euclidean neighborhood retracts, Topol- ogy4(1965), no
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Functoriality of the Klein-Williams Invariant and Universality Theory
The Klein-Williams invariant is functorial; for simply-connected spaces the universal invariant group is the free abelian group on irreducible characteristic polynomials; and ℓ_G and λ_G vanish simultaneously.