nLab
Rozansky-Witten theory

Rozansky-Witten theory, Rozansky-Witten invariant, Rozansky-Witten class

Rozansky and Witten constructed an isometry invariant of hyper-Kähler manifolds, which depends also on a trivalent graph. Kontsevich has shown an approach to Rozansky-Witten invariants via characteristic classes of foliations and Gelʹfand-Fuks cohomology. He devised a formal construction, again depending on a trivalent graph of a cohomology class of the Lie algebra of formal (in the sense of formal power series) Hamiltonian vector fields on any arbitrary finite-dimensional symplectic vector space. Characteristic classes of foliations may induce examples where this construction applies; one of the examples yields Rozansky-Witten classes.

Stimulated by Kontsevich’s 1997 letters to Victor Ginzburg and Witten, Kapranov has approached the RW invariants for all trivalent graphs at once via a single Atiyah class. This construction gives essentially a clever repackaging of the Kontsevich’s construction.

Revised on September 29, 2010 15:23:50 by Zoran Škoda (161.53.130.104)