Functoriality of the Klein-Williams Invariant and Universality Theory
Abstract
Both the Klein-Williams invariant G(f) from KW2 and the generalized equivariant Lefschetz invariant λG(f) from weber07 serve as complete obstructions to the fixed point problem in the equivariant setting. The latter is functorial in the sense of Definition functorial. The first part of this paper aims to demonstrate that G(f) is also functorial. The second part summarizes the ``universality" theory of such functorial invariants, developed in lueck1999, Weber06, and explicitly computes the group in which the universal invariant lies, under a certain hypothesis. The final part explores the relationship between G(f) and λG(f), and presents examples to compare G(f), λG(f), and the universal invariant.
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