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Given an $(m-1)$-dimensional cycle $z$ in a finitely generated acyclic chain complex, we want to explicitly construct an $m$-dimensional chain $\cob(z)$ whose algebraic boundary is $z$. Theacyclicity of the chain complex implies that a solution exists (it is not unique) but the traditionallinear algebra methods of finding it lead to a high complexity of computation. We are searching for moreefficient algorithms based on geometric considerations. The main motivation for studying this problemcomes from the topological and computational dynamics, namely, from designing general algorithmscomputing the homomorphism induced in homology by a continuous map. This, for turn, is an essential stepin computing such invariants of dynamical properties of nonlinear systems as Conley index or Lefschetznumber. Another potential motivation is in the relationship of our problem to the problem of findingminimal surfaces of closed curves.

Recursive coboundary formula for cycles in acyclic chain complexes