“Real Monomial Lefschetz Invariants”
Abstract: Let X be a finite G-set, consider the permutation RG-module M=RX and S(M) be the unit sphere of M. The reduced Lefschetz invariant for X, which is an element of the Burnside ring B(G), is defined to be λ_G(S(M))=-Σ (-1)^n [C_n] where C_n is the set of n-simplices of the triangulation of S(M). We discuss a theorem which gives the Lefschetz invariant in terms of the idempotent basis of QB(G). This has a connection with the reduced Euler characteristic of the n-sphere Sn. Then we generalize the reduced Lefschetz invariant to monomial Burnside rings and with the help of this we decompose the tom Dieck map into a product of two maps.
Date : April 29, 2009 (Wednesday)
Time : 13:40-14:30
Place: Room SAZ01