On an equivariant analogue of the monodromy zeta function

TL;DR

This paper develops an equivariant version of the monodromy zeta function for germs with finite group actions, extending classical formulas like Sebastiani-Thom and A'Campo to the equivariant setting.

Contribution

It introduces an equivariant monodromy zeta function as an element of the Grothendieck ring of finite (Z x G)-sets and formulates its key properties.

Findings

Defines an equivariant monodromy zeta function in the Grothendieck ring.

Provides equivariant analogues of Sebastiani-Thom and A'Campo formulas.

Extends classical monodromy invariants to the setting with group actions.

Abstract

We offer an equivariant analogue of the monodromy zeta function of a germ invariant with respect to an action of finite group G as an element of the Grothendieck ring of finite (Z x G)-sets. We formulate equivariant analogues of the Sebastiani-Thom theorem and of the A'Campo formula.