L-theory for local systems of homotopy coalgebras and the exact sequence for surgery

In this work various versions of L-theory for local systems of homotopy coalgebras over simplicial complexes are developed. The relation to L-theory for local systems of chain complexes is examined. We give a construction of $\Omega$-spectra whose homotopy groups are equal to the corresponding bordism groups of local systems of homotopy Poincare coalgebras. By means of these $\Omega$-spectra the exact sequence for surgery in L-theory for homotopy coalgebras is obtained.