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TOPOLOGICAL INVARIANTS OF STRATIFIED SPACES. (2 of 2)
We demonstrate that every complex in SD(X) has naturally associated Lagrangian
structures and
conversely, that Lagrangian structures serve as the natural building
blocks for objects in
SD(X). Our main result asserts that there is in fact an
equivalence of categories
between SD(X) and a twisted product of categories of
Lagrangian structures.
This may be viewed as a Postnikov system for SD(X) whose
fibers are categories of
Lagrangian structures.
We prove that the associated
signature and L-classes are independent of the choice
of Lagrangian structures, so
that singular spaces with odd codimensional strata,
such as e.g. certain
compactifications of locally symmetric spaces, have well-defined
L-classes, provided Lagrangian
structures exist.
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