M. Kontsevich proposed a topological construction for an invariant Z of rational homology 3-spheres using configuration space integrals. G. Kuperberg and D. Thurston proved that Z is a universal real finite type invariant for integral homology spheres in the sense of Ohtsuki, Habiro and Goussarov. We discuss the behaviour of Z under rational homology handlebodies replacements. The explicit formulae that we present generalize a sum formula obtained by the author for the Casson-Walker invariant in 1994. They allow us to identify the degree one term of Z with the Walker invariant for rational homology spheres.
Publié le : 2004-11-19
Classification:
3-manifolds,
configuration space integrals,
homology spheres,
finite type invariants,
Jacobi diagrams,
clovers,
claspers,
Casson-Walker invariant,
MSC 57M27 ; 57N10 55R80 57R20,
[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
@article{hal-00381903,
author = {Lescop, Christine},
title = {Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of rational homology 3-spheres},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00381903}
}
Lescop, Christine. Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of rational homology 3-spheres. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00381903/