The signature of closed oriented manifolds is well-known to be multiplicativeunder finite covers. This fails for Poincar\'e complexes as examples of C. T.C. Wall show. We establish the multiplicativity of the signature, and moregenerally, the topological L-class, for closed oriented stratifiedpseudomanifolds that can be equipped with a middle-perverse Verdier self-dualcomplex of sheaves, determined by Lagrangian sheaves along strata of oddcodimension (so-called L-pseudomanifolds). This class of spaces contains allWitt spaces and thus all pure-dimensional complex algebraic varieties. We applythis result in proving the Brasselet-Sch\"urmann-Yokura conjecture for normalcomplex projective 3-folds with at most canonical singularities, trivialcanonical class and positive irregularity. The conjecture asserts the equalityof topological and Hodge L-class for compact complex algebraic rationalhomology manifolds.
展开▼
