Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

@article{Liu2013BihamiltonianCA,
  title={Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case},
  author={Si‐Qi Liu and You-jin Zhang},
  journal={Communications in Mathematical Physics},
  year={2013},
  volume={324},
  pages={897-935}
}
We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations. 

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