Communications in Mathematical Physics

, Volume 327, Issue 2, pp 433–441 | Cite as

Formal Formality of the Hypercommutative Algebras of Low Dimensional Calabi–Yau Varieties

  • Gabriel C. Drummond-ColeEmail author


There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi–Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of the genus zero B-model. It is shown that this truncation loses no information for some cases, including all Calabi–Yau 3-folds.


Modulus Space Internal Edge Harmonic Form Formal Unit Diagonal Part 
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  1. 1.
    Barannikov S., Kontsevich M.: Frobenius manifolds and formality of Lie algebras of polyvector fields. Int. Math. Res. Not. 4, 201–215 (1998)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Drummond-Cole G.C., Vallette B.: The minimal model for the Batalin–Vilkovisky operad. Selecta Math. 19, 1–47 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Loday, J.-L., Vallette, B.: Algebraic operads. In: Grundlehren der mathematischen Wissenschaften, vol. 346. Springer, BerlinGoogle Scholar
  4. 4.
    Getzler, E.: Operads and moduli spaces of genus 0 Riemann surfaces. In: The Moduli Space of Curves. Progress in Mathematics, vol. 129, pp. 199–230. Birkhäuser, Boston (1995)Google Scholar
  5. 5.
    Getzler E.: Batalin–Vilkovisky algebras and two-dimensional topological field theories. Comm. Math. Phys. 159, 265–285 (1994)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Galvez-Carrillo I., Tonks A., Vallette B.: Homotopy Batalin–Vilkovisky algebras. J. Noncommut. Geom. 6, 539–602 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Griffiths P., Harris J.: Principles of Algebraic Geometry. Wiley, New York (1978)zbMATHGoogle Scholar
  8. 8.
    Merkulov S.: Strongly homotopy algebras of a Kähler manifold. Int. Math. Res. Not. 1999, 153–164 (1998)CrossRefGoogle Scholar
  9. 9.
    Park J.-S.: Semi-classical quantum fields theories and Frobenius manifolds. Lett. Math. Phys. 81, 41–59 (2007)ADSCrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Center for Geometry and PhysicsInstitute for Basic Science (IBS)PohangRepublic of Korea

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