# The L-class of non-Witt spaces | Annals of Mathematics

Abstract Characteristic classes for oriented pseudomanifolds can be defined using appropriate self-dual complexes of sheaves. On non-Witt spaces, self-dual complexes compatible to intersection homology are determined by choices of Lagrangian structures at the strata of odd codimension. We prove that the associated signature and \rm 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 \rm L-classes, provided Lagrangian structures exist. We illustrate the general results with the example of the reductive Borel-Serre compactification of a Hilbert modular surface.

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### 数学年刊（Annals of Mathematics）

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