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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ k$-flat structures and exotic characteristic classes


Author: Lisa R. Goldberg
Journal: Trans. Amer. Math. Soc. 306 (1988), 433-453
MSC: Primary 57R32; Secondary 57R20
DOI: https://doi.org/10.1090/S0002-9947-1988-0933300-6
MathSciNet review: 933300
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Abstract: We generalize the concept of "foliation" and define $ k$-flat structures; these are smooth vector bundles with affine connections whose characteristic forms vanish above a certain dimension. Using semisimplicial techniques we construct a classifying space for $ k$-flat structures, and prove a classification theorem for these structures on smooth manifolds.

Techniques from rational homotopy theory are used to relate the exotic characteristic classes of foliations to the rational homotopy groups and cohomology of the classifying space.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0933300-6
Article copyright: © Copyright 1988 American Mathematical Society