|
TOPOLOGICAL INVARIANTS OF STRATIFIED SPACES. (1 of 2)
Intersection homology theory provides a way to obtain generalized Poincaré
duality,
as well as a signature
and characteristic classes, for singular spaces. For this to
work, one has had to
assume however that the space satisfies the so-called Witt
condition. We extend this
approach to constructing invariants to spaces more general
than Witt spaces.
We present an algebraic
framework for extending generalized Poincaré duality and
intersection homology to
singular spaces X not necessarily Witt. The initial step in
this program is to define
the category SD(X) of complexes of sheaves suitable for
studying intersection
homology type invariants on non-Witt spaces. The objects in
this category can be
shown to be the closest possible self-dual "approximation'' to
intersection chain
sheaves. It is therefore desirable to understand the structure of
such self-dual sheaves
and to isolate the minimal data necessary to construct them.
As the main tool in this
analysis we introduce the notion of a Lagrangian structure.
More...
Back.
| 
