Lie algebras of symplectic derivations and cycles on the moduli spaces

Details Lie algebras of symplectic derivations and cycles on the moduli spaces Lie algebras of symplectic derivations and cycles on the moduli spaces

2006-08-28

arxiv.org/abs/math/0608673v2

Geom. Topol. Monogr. 13 (2008) 335-354

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 25 February 2008

Scientific paper

10.2140/gtm.2008.13.335

We consider the Lie algebra consisting of all derivations on the free
associative algebra, generated by the first homology group of a closed oriented
surface, which kill the symplectic class. We find the first non-trivial
abelianization of this Lie algebra and discuss its relation to unstable
cohomology classes of the moduli space of curves via a theorem of Kontsevich.

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