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On an equivariant version of the zeta function of a transformationстатья
- Авторы: Gusein-Zade S.M., Luengo I., Melle-Hernández A.
- Журнал: Arnold Mathematical Journal
- Том: 1
- Номер: 2
- Год издания: 2015
- Первая страница: 127
- Последняя страница: 140
- DOI: 10.1007/s40598-015-0012-8
- Аннотация: 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 use 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 itself. 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.
- Добавил в систему: Гусейн-Заде Сабир Меджидович