A formal moduli space of symplectic connections of Ricci-type on T2n

✍ Scribed by M. Cahen; S. Gutt; J. Horowitz; J. Rawnsley

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 144 KB
• Volume: 46
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00131-6

✦ Synopsis

We consider analytic curves ∇ t of symplectic connections of Ricci-type on the torus T 2n with ∇ 0 the standard connection. We show, by a recursion argument, that if ∇ t is a formal curve of such connections then there exists a formal curve of symplectomorphisms ψ t such that ψ t • ∇ t is a formal curve of flat T 2n -invariant symplectic connections and so ∇ t is flat for all t. Applying this result to the Taylor series of the analytic curve, it means that analytic curves of symplectic connections of Ricci-type starting at ∇ 0 are also flat.

The group G of symplectomorphisms of the torus (T 2n , ω) acts on the space E of symplectic connections which are of Ricci-type. As a preliminary to study the moduli space E/G we study the moduli of formal curves of connections under the action of formal curves of symplectomorphisms.