Title: Amazing consequences of simple properties of the trace
Speaker: Kate Ponto
Speaker Info: University of Kentucky
For a fibration (with a connected base space) the Euler characteristic of the total space is the product of the Euler characteristics of the base and the fiber. The Euler characteristic is also additive on subcomplexes. Combining these we have a description of the Euler characteristic of a G-space in terms of the quotients of the isotropy subspaces. The generalizations of the Euler characteristic to fixed point invariants, primarily the Lefschetz number and Reidemeister trace, are similarly additive and multiplicative and the equivariant Lefschetz number and Reidemeister trace have corresponding isotropy decompositions.Date: Monday, March 2, 2015
Remarkably, the additivity and multiplicativity results are consequences of a simple formal observation (and some significant topological input). Once in place, these results give a particularly transparent comparison of various interpretations of equivariant fixed point invariants.