In this paper we have developed a general theory of characteristic classes of modules. To a given invariant map defined on a Lie algebra, we associate a cohomology class by using the curvature form of a certain kind of connections. Here we present a very simple proof of the invariance theorem (Theorem 12), which states that equivalent connections give rise to the same characteristic class. We have used those invariant maps of {9} to define Chern classes of projective modules and we have derived their basic properties. It might be interesting to observe that this theory could be applied to define characteristic classes of bilinear maps. In particular, the Euler classes of {6} can be obtained in this way.
| Identifer | oai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:123456789/97347 |
| Date | 25 September 2017 |
| Creators | Kong, Maynard |
| Publisher | Pontificia Universidad Católica del Perú |
| Source Sets | Pontificia Universidad Católica del Perú |
| Language | Español |
| Detected Language | English |
| Type | Artículo |
| Format | |
| Source | Pro Mathematica; Vol. 22, Núm. 43-44 (2008); 51-65 |
| Rights | Artículo en acceso abierto, Attribution 4.0 International, https://creativecommons.org/licenses/by/4.0/ |
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