### Bordism of automorphisms from the algebraic L-theory point of view, by Andrew Ranicki

The mapping torus construction defines a natural transformation T from
the bordism over a space X of n-dimensional manifolds M with an automorphism
f:M-->M to the bordism of (n+1)-dimensional manifolds N over XxS^1.
Quinn used open book surgery to identify the fibre of T (in dimensions n>5)
with the asymmetric Witt theory of the fundamental group ring Z[\pi_1(X)].
In this paper the fibre of T is identified with the quadratic Wall L-theory
of the localization \Omega^{-1}Z[\pi_1(XxS^1)] inverting the set \Omega of
square matrices in the Laurent polynomial ring
Z[\pi_1(XxS^1)]=Z[\pi_1(X)][z,z^{-1}] which present f.g. projective
Z[\pi_1(X)]-modules. The essential ingredient is the observation that
the canonical infinite cyclic cover of a finite CW complex N with
\pi_1(N)=\pi_1(XxS^1) is finitely dominated if and only if
H_*(N;\Omega^{-1}Z[\pi_1(XxS^1)])=0.

Andrew Ranicki <a.ranicki@edinburgh.ac.uk>