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Transactions of the American Mathematical Society

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

 

 

Slicing and intersection theory for chains modulo $ \nu $ associated with real analytic varieties


Author: Robert M. Hardt
Journal: Trans. Amer. Math. Soc. 183 (1973), 327-340
MSC: Primary 32C05; Secondary 32B20
MathSciNet review: 0338430
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Abstract: In a real analytic manifold a k dimensional (real) analytic chain is a locally finite sum of integral multiples of chains given by integration over certain k dimensional analytic submanifolds (or strata) of some k dimensional real analytic variety. In this paper, for any integer $ \nu \geq 2$, the concepts and results of [6] on the continuity of slicing and the intersection theory for analytic chains are fully generalized to the modulo $ \nu $ congruence classes of such chains.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0338430-7
Keywords: Analytic chain (modulo $ \nu $), slice (modulo $ \nu $), support (modulo $ \nu $), dimension, intersection theory, flat chain (modulo $ \nu $), rectifiable current, mass
Article copyright: © Copyright 1973 American Mathematical Society