Witt groups of constructible derived categories
(joint work with Joerg Schuermann, Muenster)
Let X be a space with a chosen family of stratifications, e.g.
analytic, algebraic, PL,... The constructible derived category of X
captures that part of the topology which is visible to the chosen
family of stratifications. It is a triangulated category with
duality, given by the Poincare-Verdier dual. Any such category has 4-
periodic Witt groups, defined by Balmer (roughly, these are a
quadratic version of the K-theory of the category). I will review the
construction of these groups, and explain how they can be viewed as
an algebraic model of the bordism theory of certain spaces over X. I
will then explain how this picture leads to complementary algebraic
and geometric proofs of (a strong form of) a theorem of Cappell and
Shaneson generalising Novikov additivity.