The Euler characteristic of graph complexes via Feynman diagrams

Details The Euler characteristic of graph complexes via Feynman diagrams The Euler characteristic of graph complexes via Feynman diagrams

2004-12-05

arxiv.org/abs/math/0412094v2

Mathematics

Quantum Algebra

12 pages, 2 figures; v2: added missing references

Scientific paper

We prove several claims made by Kontsevich about the orbifold Euler characteristic of the three types of graph homology introduced by him. For this purpose, first we develop a simplified version of the Feynman diagram method, which requires integrals in one variable only, to obtain the generating functions as asymptotic expansions of certain Gaussian integrals. Finally, following Penner, we relate these integrals to the gamma function in order to compute the individual coefficients of the generating functions.

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