Acta Mathematica Sinica

, Volume 15, Issue 1, pp 53–80

On the equivalence of multiplicative structures in floer homology and quantum homology

  • Gang Liu
  • Gang Tian

DOI: 10.1007/s10114-999-0060-x

Cite this article as:
Liu, G. & Tian, G. Acta Math Sinica (1999) 15: 53. doi:10.1007/s10114-999-0060-x


In this paper, we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring. We will also prove that GW-invariants in Floer homology and quantum homology are equivalent.


Floer homologyQuantum homologyGW-invariantsJ-holomorphic curvesModuli space

1991MR Subject Classification


Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Gang Liu
    • 1
  • Gang Tian
    • 2
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of MathematicsMITCambridgeUSA