Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 8 (2012), 076, 7 pages      arXiv:1210.5320      http://dx.doi.org/10.3842/SIGMA.2012.076
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”

Recursion Operators and Frobenius Manifolds

Franco Magri
Dipartimento di Matematica ed Applicazioni, Università degli Studi di di Milano Bicocca, Via Roberto Cozzi 53, 20125 Milano, Italy

Received June 01, 2012, in final form October 05, 2012; Published online October 19, 2012

Abstract
In this note I exhibit a ''discrete homotopy'' which joins the category of F-manifolds to the category of Poisson-Nijenhuis manifolds, passing through the category of Frobenius manifolds.

Key words: F-manifolds; Frobenius manifolds; Poisson-Nijenhuis manifolds.

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References

  1. Hertling C., Manin Y., Weak Frobenius manifolds, Int. Math. Res. Not. 1999 (1999), no. 6, 277-286, math.QA/9810132.
  2. Hertling C., Frobenius manifolds and moduli spaces for singularities, Cambridge Tracts in Mathematics, Vol. 151, Cambridge University Press, Cambridge, 2002.
  3. Dubrovin B., Geometry of 2D topological field theories, in Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math., Vol. 1620, Springer, Berlin, 1996, 120-348, hep-th/9407018.
  4. Kosmann-Schwarzbach Y., Magri F., Poisson-Nijenhuis structures, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), 35-81.

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