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Transactions of the American Mathematical Society

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



The existence of combinatorial formulae for characteristic classes

Authors: Norman Levitt and Colin Rourke
Journal: Trans. Amer. Math. Soc. 239 (1978), 391-397
MSC: Primary 57D20; Secondary 57C05
MathSciNet review: 0494134
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Abstract: Given a characteristic class on a locally ordered combinatorial manifold M there exists a cocycle which represents the class on M and is locally defined, i.e. its value on $\sigma \in M$ depends only on the ordered star ${\text {st}}(\sigma ,M)$. For rational classes the dependence on order disappears. There is also a locally defined cycle which carries the dual homology class.

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Keywords: Combinatorial formula, characteristic class, Pontrjagin class, local formula, classifying block bundle
Article copyright: © Copyright 1978 American Mathematical Society