nLab
Gauss-Manin connection

In the context of families of algebraic varieties, the cohomology classes vary with families in a way which induces a specific kind of flat connections. The most important case is in Picard-Fuchs theory.

  • wikipedia Gauss-Manin connection

  • Yu. I. Manin, Algebraic curves over fields with differentiation, Izv. Akad. Nauk SSSR Ser. Mat., 22:6 (1958), 737–756, pdf(in Russian)

  • Boris Tsygan, On the Gauss-Manin connection in cyclic homology, Methods Funct. Anal. Topology 13 (2007), no. 1, 8394.

  • Ezra Getzler, Cartan homotopy formulas and the Gauss/manin connection in cyclic homology, pdf

There is a version in noncommutative setup.

  • V. Dolgushev, D. Tamarkin, B. Tsygan, Noncommutative calculus and the Gauss-Manin connection, arxiv/0902.2202
Revised on October 26, 2011 01:02:33 by Zoran Škoda (161.53.130.104)