Topology 41 (2002) 1031–1040 Lefschetz numbers of iterates of the monodromy and truncated arcs Jan Denef a ; 1 , Fran'cois Loeser b; ?; 2 a Department of Mathematics, University of Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium b Departement de Mathematiques et Applications, Ecole Normale Superieure, 45 Rue d'Ulm, 75230 Paris Cedex 05, France Received 14 January 2000; accepted 26 February 2001 Abstract We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs. We also construct a canonical representative of the Milnor /bre in a suitable monodromic Grothendieck group. ? 2002 Elsevier Science Ltd. All rights reserved. MSC: 14B05; 14J17; 32S25; 32S55 Keywords: Monodromy; Milnor /bre; Arcs; Singularities; Lefschetz numbers; Motivic integration; Monodromic Grothendieck group 1. Introduction Let X be a smooth complex algebraic variety and let f : X ? C be a non constant morphism of complex algebraic varieties. We /x a smooth metric on X . Let x be a point of f ?1 (0).
- characteristic zero
- group generated
- involve truncated
- arcs modulo
- arc
- taking euler characteristic
- truncated arcs
- grothendieck group