In addition they defined a notion of twisted Chern character which is a characteristic class for an element of twisted K-theory.
22.
In the early 1950s it concerned what are now called Thom spaces, characteristic classes, cobordism theory, and the Thom transversality theorem.
23.
Thus, the cohomology dimension of the stable normal bundle, as detected by its highest non-vanishing characteristic class, is an obstruction to immersions.
24.
The characteristic class approach to curvature invariants was a particular reason to make a theory, to prove a general Gauss Bonnet theorem.
25.
The theory of characteristic classes of smooth manifolds has been extended to spectral triples, employing the tools of operator K-theory and cyclic cohomology.
26.
The formula also expresses in a precise way the vague notion that the Todd classes are in some sense reciprocals of characteristic classes.
27.
It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest.
28.
There are several other types of characteristic classes for vector bundles that take values in cohomology, including Chern classes, Stiefel Whitney classes, and Pontryagin classes.
29.
In work with Ib Madsen, he resolved the Mumford Conjecture about rational characteristic classes of surface bundles in the limit as the genus tends to infinity.
30.
In a discussion of curvature representation of characteristic classes of principal bundles ( Chern Weil theory ), it covers Euler classes, Chern classes, and Pontryagin classes.
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