Theory of valuations on manifolds, IV. New properties of the multiplicative structure

S. Alesker*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This is the fourth part in the series of articles [A4], [A5], [AF] (see also [A3]) where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations is compatible with the product. Then it is proved that the Euler-Verdier involution on smooth valuations is an automorphism of the algebra of valuations. Then an integration functional on valuations with compact support is introduced, and a property of selfduality of valuations is proved. Next a space of generalized valuations is defined, and some basic properties of it are proved. Finally a canonical imbedding of the space of constructible functions on a real analytic manifold into the space of generalized valuations is constructed, and various structures on valuations are compared with known structures on constructible functions.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2004-2005
PublisherSpringer Verlag
Number of pages44
ISBN (Print)3540720529, 9783540720522
StatePublished - 2007

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434


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