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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Theory of valuations on manifolds, III. Multiplicative structure in the general case


Authors: Semyon Alesker and Joseph H. G. Fu
Journal: Trans. Amer. Math. Soc. 360 (2008), 1951-1981
MSC (2000): Primary 52B45, 52A39, 53C65
Published electronically: November 27, 2007
MathSciNet review: 2366970
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Abstract: This is the third part of a series of articles where the theory of valuations on manifolds is constructed. In the second part of this series the notion of a smooth valuation on a manifold was introduced. The goal of this article is to put a canonical multiplicative structure on the space of smooth valuations on general manifolds, thus extending some of the affine constructions from the first author's 2004 paper and, from the first part of this series.


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Additional Information

Semyon Alesker
Affiliation: Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
Email: semyon@post.tau.ac.il

Joseph H. G. Fu
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: fu@math.uga.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04489-3
PII: S 0002-9947(07)04489-3
Received by editor(s): October 21, 2005
Received by editor(s) in revised form: December 2, 2005
Published electronically: November 27, 2007
Additional Notes: The first author was partially supported by ISF grant 1369/04.
The second author was partially supported by NSF grant DMS-0204826.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.