ИСТИНА |
Войти в систему Регистрация |
|
Интеллектуальная Система Тематического Исследования НАукометрических данных |
||
It is known that the Alexander polynomial in several variables of an algebraic link determines the embedded topology of the corresponding plane curve singularity. The Alexander polynomial coincides with the Poincaré series of the multi-index filtration defined by the valuations corresponding to the branches of the curve. Thus the Poincaré series (of a natural filtration) determines the topology of a plane curve singularity. We shall discuss equivariant (with respect to a finite group action) analogue of these statements. There exist several concepts of an equivariant (with respect to a finite group action) version of the Poincaré series of a filtration. One of them is defined as a power series in several variables with the coefficients from a certain modification of the Burnside ring of the group. It was shown that (modulo simple exceptions) the equivariant Poincaré series determines the equivariant topology of the plane curve singularity. The talk is based on joint works with A.Campillo and F.Delgado.