Subject: Question on Poincare series for the Topology list
Date: Tue, 14 May 2002 16:38:37 +0100
From: Martin Crossley
In trying to find a painless way of introducing
British undergraduates to homology, I hit the
following problem:
Suppose you have three graded vector spaces (with
Poincare series P_1, P_2, P_3) which are linked by
a long exact sequence (like the homology exact
sequence of a pair). Then you have an equation like
P_2(-1) = P_3(-1) + P_1(-1).
But this does not contain as much information as
the exact sequence, even if you suppose no knowledge
of the morphisms.
Is there a formula in the Poincare series that
catches more of the information ?
Martin Crossley