2000/10/09 by Marius Crainic, Crainic, Marius
Mathematics · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG) #math.AT #math.DG #math.KT #math.SG
paper · pdf · doi:10.48550/arxiv.math/0010085
12 pages
arxiv created 2000/12/11 · arxiv updated 2009/11/30
In this note we clarify the relevance of ``connections up to homotopy'' to the theory of characteristic classes. We have already remarked \citeCrai that such connections up to homotopy can be used to compute the classical Chern characters. Here we present a slightly different argument for this, and then proceed with the discussion of the flat (secondary) characteristic classes. As an application, we clarify the relation between the two different approaches to characteristic classes of algebroids (and of Poisson manifolds in particular): we explain that the intrinsic characteristic classes are precisely the secondary classes of the adjoint representation.