The L-class of non-Witt spaces

• 成果类型: Article
• 署名作者: Banagl, Markus
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.743
• 发表日期: 2006
• 页码: 743-766
• 关键词: spectral geometry; HOMOLOGY

摘要

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 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. ate the general provided Lagrangian structures exist. We illustrate results with the example of the reductive Borel-Serre compactification of a Hilbert modular surface.