On an equivariant version of the zeta function of a transformation

Details On an equivariant version of the zeta function of a transformation On an equivariant version of the zeta function of a transformation

2012-03-15

arxiv.org/abs/1203.3344v1

Mathematics

Algebraic Geometry

arXiv admin note: text overlap with arXiv:0803.3708

Scientific paper

Earlier the authors offered an equivariant version of the classical monodromy zeta function of a G-invariant function germ with a finite group G as a power series with the coefficients from the Burnside ring of the group G tensored by the field of rational numbers. One of the main ingredients of the definition was the definition of the equivariant Lefschetz number of a G-equivariant transformation given by W.L\"uck and J.Rosenberg. Here we offer another approach to a definition of the equivariant Lefschetz number of a transformation and describe the corresponding notions of the equivariant zeta function. This zeta-function is a power series with the coefficients from the Burnside ring of the group G. We give an A'Campo type formula for the equivariant monodromy zeta function of a function germ in terms of a resolution.

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