RT Journal Article
T1 The Denef-Loeser zeta function is not a topological invariant
A1 Artal Bartolo, Enrique
A1 Cassou-Noguès, Pierrette
A1 Luengo Velasco, Ignacio
A1 Melle Hernández, Alejandro
AB An example is given which shows that the Denef–Loeser zeta function (usually called the topological zeta function) associated to a germ of a complex hypersurface singularity is not a topological invariant of the singularity. The idea is the following. Consider two germs of plane curves singularities with the same integral Seifert form but with different topological type and which have different topological zeta functions. Make a double suspension of these singularities (consider them in a 4-dimensional complex space). A theorem of M. Kervaire and J. Levine states that the topological type of these new hypersurface singularities is characterized by their integral Seifert form. Moreover the Seifert form of a suspension is equal (up to sign) to the original Seifert form. Hence these new singularities have the same topological type. By means of a double suspension formula the Denef–Loeser zeta functions are computed for the two 3-dimensional singularities and it is verified that they are not equal.
PB Oxford University Press
SN 0024-6107
YR 2002
FD 2002-02
LK https://hdl.handle.net/20.500.14352/57596
UL https://hdl.handle.net/20.500.14352/57596
LA eng
NO During the development of this paper, the second author wasthe guest of the Department of Algebra at the University Complutense of Madrid, supported by a sabbatical grant from the MEC. She wishes to thanks the MEC for its support and the members of the Department of Algebra for their warmhospitality.
NO DGES
NO MEC
DS Docta Complutense
RD 10 may 2025