2012/03/15 by S. M. Gusein‐Zade, S. M. Gusein-Zade, I. Luengo +5
Mathematics · #32S05 #32S50 #57R91 #58K10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:32S05 #msc:32S50 #msc:57R91 #msc:58K10
paper · pdf · doi:10.48550/arxiv.1203.3344
arXiv admin note: text overlap with arXiv:0803.3708 . This is an improved revised version of the paper including a new section where orbifold versions of the Lefschetz number and of the monodromy zeta function corresponding to the two equivariant ones are discussed
openalex publication_date 2012/03/15 · arxiv created 2013/03/14 · arxiv updated 2013/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.Lück 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. Finally we discuss orbifold versions of the Lefschetz number and of the monodromy zeta function corresponding to the two equivariant ones.