2,718 research outputs found
Wall's finiteness obstruction
The purpose of this note is to give a self contained description of Walls
finiteness obstruction
Topological Equivalence of Linear Representations for Cyclic Groups, I & II
In the two parts of this paper we solve a problem of De Rham, proving that
Reidemeister torsion invariants determine topological equivalence of linear
G-representations, for G a finite cyclic group. Methods in controlled K-theory
and surgery theory are developed to establish, and effectively calculate, a
necessary and sufficient condition for non-linear similarity in terms of the
vanishing of certain non-compact transfer maps. For cyclic groups of 2-power
order, we obtain a complete classification of non-linear similarities.Comment: The first version of this paper appeared as MPI Preprint 1997-58, Max
Planck Institut fuer Mathematik, Bonn. The final version includes many
improvements in exposition and new results. It is now divided into two parts.
Part I (36 pages) will appear in Annals of Mathematics, and Part II (43
pages) will appear in Forum Mat
Stability in controlled L-theory
We prove a squeezing/stability theorem for delta-epsilon controlled L-groups
when the control map is a fibration on a finite polyhedron. A relation with
boundedly-controlled L-groups is also discussed.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
More examples of discrete co-compact group actions
We survey some results and questions about free actions of infinite groups on
products of spheres and euclidean spaces, and give some new co-compact
examples
Controlled surgery with trivial local fundamental groups
We provide a proof of the controlled surgery sequence, including stability,
in the special case that the local fundamental groups are trivial. Stability is
a key ingredient in the construction of exotic homology manifolds by Bryant,
Ferry, Mio and Weinberger, but no proof has been available. The development
given here is based on work of M. Yamasaki.Comment: 5 page
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