JP Journal of Geometry and Topology
Volume 2, Issue 1, Pages 15 - 28
(March 2002)
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A GEOMETRICAL CONSTRUCTION OF THE FINITENESS OBSTRUCTION TO SPLITTING
Jerzy Dydak (USA)
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modules it leads to a natural group structure equivalent to the reduced
projective class group
Thus each idempotent f
has a natural obstruction
to be stably equivalent to an
identity idempotent. In the case of homotopy category of pointed, finite, and
connected CW complexes, each idempotent f has
an obstruction
to split (see the work of Lück and
Ranicki [7]). It is shown that a generic idempotent is an idempotent on an n-dimensional
CW complex X
so that
In that case
is equal to
where
is the induced idempotent of
cellular n-chains of the universal
cover
of X.
