Algebraic L-spectra and the assembly map

An algebraic Poincare complex over a ring with involution A
is an A-module chain complex with Poincare duality, such as is exhibited by a chain complex of a manifold. The algebraic Poincare cobordism groups are the Wall surgery obstruction groups L_*(A),
Even after 45 years the L-groups are somewhat mysterious, with
deep significance in the topology of manifolds. The cobordism group \Omega_n of n-dimensional manifolds is the nth homotopy group \pi_n(\Omega) of the simplicial set in which the k-simplexes are the k-dimensional manifolds M with boundary and a transverse map (M,\partial M) --> (\Delta^k,\partial \Delta^k). There is an entirely analogous construction of a simplicial set L(A) in the world of algebraic Poincare complexes, with \pi_n(L(A))=L_n(A).
It is a consequence of the celebrated 1969 work of Kirby and
Siebenmann that L(Z) is homotopy equivalent to L_0(Z) \times G/TOP,
with G/TOP the classifying space for fibre homotopy trivialized
topological bundles. L(A) is the 0th space of an \Omega-spectrum, also denoted L(A). The main result of the talk will be an identification of the generalized homology groups H_*(X;L(Z)) of a simplicial complex X with the algebraic Poincare cobordism groups of the additive category of (Z,X)-modules with a chain duality involution, and the construction of the assembly map A : H_*(X;L(Z)) --> L_*(Z[\pi_1(X)]) appearing in the algebraic surgery exact sequence for the topological manifold structure set. Most - but not all - of the material in the talk has already appeared in my 1992 book "Algebraic L-theory and topological manifolds"
http://www.maths.ed.ac.uk/~aar/books/topman.pdf