“Real Monomial Lefschetz
Invariants”

IPEK TUVAY

(BILKENT UNIVERSITY)

__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 S^{n}.
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