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Knots, Singular Embeddings, and Monodromy

  • Markus BanaglEmail author
  • Sylvain E. Cappell
  • Julius L. Shaneson
Chapter
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 1)

Abstract

The Goresky-MacPherson L-class of a PL pseudomanifold piecewise-linearly embedded in a PL manifold in a possibly nonlocally flat way, can be computed in terms of the Hirzebruch-Thom L-class of the manifold and twisted L-classes associated to the singularities of the embedding, as was shown by Cappell and Shaneson. These formulae are refined here by analyzing the twisted classes. We treat the case of Blanchfield local systems that extend into the singularities as well as cases where they do not extend. In the latter situation, we consider fibered embeddings of strata and 4-dimensional singular sets, using work of Banagl. Rho-invariants enter the picture.

Keywords

Local System Real Vector Space Cyclic Cover Constant Sheaf Seifert Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Markus Banagl
    • 1
    Email author
  • Sylvain E. Cappell
    • 2
  • Julius L. Shaneson
    • 3
  1. 1.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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