On the quantum homology algebra of toric fano manifolds

Yaron Ostrover, Ilya Tyomkin

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume15
Issue number1
DOIs
StatePublished - Jun 2009
Externally publishedYes

Keywords

  • Quantum homology
  • Semisimplicity
  • Toric fano manifolds

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