Title: Topological and Hodge L-Classes of Singular Covering Spaces and Varieties with Trivial Canonical Class,
Abstract: The signature of closed oriented manifolds is well-known to be multiplicative
under finite covers. This fails for Poincaré complexes as examples of C. T.
C. Wall show. We establish the multiplicativity of the signature, and more
generally, the topological L-class, for closed oriented stratified
pseudomanifolds that can be equipped with a middle-perverse Verdier self-dual
complex of sheaves, determined by Lagrangian sheaves along strata of odd
codimension (so-called L-pseudomanifolds). This class of spaces contains all
Witt spaces and thus all pure-dimensional complex algebraic varieties. We apply
this result in proving the Brasselet-Schürmann-Yokura conjecture for normal
complex projective 3-folds with at most canonical singularities, trivial
canonical class and positive irregularity. The conjecture asserts the equality
of topological and Hodge L-class for compact complex algebraic rational
homology manifolds.