Chern-Simons forms for R-linear connections on Lie algebroids
Bogdan Balcerzak
TL;DR
This paper develops a generalized Chern-Simons formula for R-linear connections on Lie algebroids, enabling the definition of characteristic classes and secondary invariants in this geometric context.
Contribution
It introduces a new generalized Chern-Simons formula for R-linear connections on Lie algebroids, expanding the toolkit for studying their characteristic classes.
Findings
Derived a generalized Chern-Simons formula for R-linear connections.
Defined Chern character and secondary characteristic classes for Lie algebroids.
Extended classical geometric invariants to the setting of Lie algebroids.
Abstract
The Chern-Simons forms for R-linear connections on Lie algebroids are considered. A generalized Chern-Simons formula for such R-linear connections is obtained. We it apply to define Chern character and secondary characteristic classes for R-linear connections of Lie algebroids.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons · Advanced Topics in Algebra