Abstract
Intersection homology enables the definition of a twisted signature of a stratified pseudomanifold with coefficients in a local system that is typically only given on the top stratum. If the local system extends to the entire space, then the twisted signature can be computed by a version of a characteristic class formula first observed by Atiyah for smooth fiber bundles. In the first part of this paper, we construct examples of singular spaces, equipped with local systems that do not extend, such that the above characteristic class formula fails. In the second part, we consider smooth codimension two embeddings of manifolds. We view the target as a stratified space with bottom stratum the image of the embedding and top stratum the complement. When the embedded manifold is a sphere, we establish various formulae that compute the twisted signature even when the local system does not extend from the top stratum to the entire space.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
