The linearity of fixed point invariants

Kate Ponto, Michael Shulman

Published 2014-06-30, updated 2017-09-26Version 2

We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of these theorems are essentially formal, taking place in the abstract context of bicategorical traces. This makes it straightforward to generalize the theory to analogous invariants in other contexts, such as equivariant and fiberwise homotopy theory.