On the quantum homology algebra of toric fano manifolds

Yaron Ostrover*, Ilya Tyomkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study certain algebraic properties of the small quantum homology algebra for the class of symplectic toric Fano manifolds. In particular, we examine the semisimplicity of this algebra, and the more general property of containing a field as a direct summand. Our main result provides an easily verifiable sufficient condition for these properties which is independent of the symplectic form. Moreover, we answer two questions of Entov and Polterovich negatively by providing examples of toric Fano manifolds with non-semisimple quantum homology, and others in which the Calabi quasi-morphism is not unique.

Original languageEnglish
Pages (from-to)121-149
Number of pages29
JournalSelecta Mathematica, New Series
Issue number1
StatePublished - Jun 2009
Externally publishedYes


FundersFunder number
National Science FoundationDMS-0706976
Directorate for Mathematical and Physical Sciences0706976


    • Quantum homology
    • Semisimplicity
    • Toric fano manifolds


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