A. S. Mishchenko, P. S. Popov
abstract:
The signature of the Poincare duality of compact topological manifolds with
local system of coefficients can be described as a natural invariant of
nondegenerate symmetric quadratic forms defined on a category of infinite
dimensional linear spaces. The objects of this category are linear spaces of the
form W = V oplus V* where V is an abstract linear space with
countable base. The space W is considered with minimal natural topology. The
symmetric quadratic form on the space W is generated by the Poincare duality
homomorphism on the abstract cochain group induced by nerves of the system of
atlases of charts on the topological manifold.