Geodesic
A~Theory of Almost Algebraic Poincar\'e Complexes
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 294-322

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Theories of almost acyclic chain complexes and of almost algebraic Poincaré complexes are constructed. These theories can be used to obtain signature invariants of combinatorial manifolds with arbitrary finite-dimensional vector bundles. 
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     author = {A. S. Mishchenko},
     title = {A~Theory of {Almost} {Algebraic} {Poincar\'e} {Complexes}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {294--322},
     publisher = {mathdoc},
     volume = {231},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2000_231_a10/}
}
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A. S. Mishchenko. A~Theory of Almost Algebraic Poincar\'e Complexes. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 294-322. http://geodesic.mathdoc.fr/item/TM_2000_231_a10/