Recently S. A. Merkulov established a link between differential geometry and homological algebra by giving descriptions of several differential geometric structures in terms of minimal resolutions of props. In particular he described the prop profile of Poisson geometry. In this paper we define a prop such that representations of its minimal resolution in a vector space V are in a one-to-one correspondence with bi-Hamiltonian structures, i.e., pairs of compatible Poisson structures, on the formal manifold associated to V.
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Henrik Strohmayer, Prop profile of bi-Hamiltonian structures. J. Noncommut. Geom. 4 (2010), no. 2, pp. 189–235DOI 10.4171/JNCG/53