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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0494134-6
PII: S 0002-9947(1978)0494134-6
Keywords: Combinatorial formula, characteristic class, Pontrjagin class, local formula, classifying block bundle
Article copyright: © Copyright 1978 American Mathematical Society