Characteristic classes for the deformation of flat connections

Author:
Huei Shyong Lue

Journal:
Trans. Amer. Math. Soc. **217** (1976), 379-393

MSC:
Primary 57D30

MathSciNet review:
0402774

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Abstract: In this paper, we study the secondary characteristic classes derived from flat connections. Let *M* be a differential manifold with flat connection . If *f* is a diffeomorphism of *M*, then is another flat connection. Denote by the difference of these two connections. Then and its exterior covariant derivative are both tensorial forms on *M*. To each invariant polynomial of , where is a globally defined form on *M*. The class for gives rise to an obstruction of the deformability from to . In particular, we prove that and connections, in the sense of E. Cartan, cannot be deformed to each other.

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DOI:
https://doi.org/10.1090/S0002-9947-1976-0402774-3

Article copyright:
© Copyright 1976
American Mathematical Society