A survey of characteristic classes of singular spaces

By Joerg Schuermann, Shoji Yokura. 2005

68 citations recorded by the source corpus.

A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a systematic study of singular spaces such as singular algebraic varieties. We make a quick survey of characteristic classes of singular varieties, mainly focusing on the functorial aspects of some important ones such as the singular versions of the Chern class, the Todd class and the Thom--Hirzebruch's L-class. Then we explain our recent "motivic" characteristic classes, which in a sense unify these three different theories of characteristic classes. We also discuss bivariant versions of them and characteristic classes of proalgebraic varieties, which are related to the motivic measures/integrations. Finally we explain some recent work on "stringy" versions of these theories, together with some references for "equivariant" counterparts.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/efd6252277ed37ac88eb7dd975936b0cab8d4d5c

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In Discrete Mathematics and Combinatorics

  1. Joerg Schuermann
  2. Laurentiu G. Maxim

In Geometry and Topology

  1. Joerg Schuermann
  2. Laurentiu G. Maxim
  3. J. Shaneson
  4. Sylvain E. Cappell
  5. M. A. Cataldo
  6. L. Migliorini

In Mathematical Physics

  1. Joerg Schuermann
  2. Laurentiu G. Maxim
  3. J. Shaneson
  4. Sylvain E. Cappell
  5. M. A. Cataldo
  6. L. Migliorini

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