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Leafwise homotopy equivalences and leafwise Sobolov spaces

Published online by Cambridge University Press:  21 November 2011

Moulay-Tahar Benameur  and
James L. Heitsch
Moulay-Tahar Benameur
Affiliation:
Université de Metz, ISGMP, Francebenameur@univ-metz.fr
James L. Heitsch
Affiliation:
Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, USAheitsch@math.uic.edu Mathematics, Northwestern University, USAj-heitsch@northwestern.edu
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Abstract

We prove that a leafwise homotopy equivalence between compact foliated manifolds induces a well defined bounded operator between all Sobolov spaces of leafwise (for the natural foliations of the graphs of the original foliations) differential forms with coefficients in a leafwise flat bundle. We further prove that the associated map on the leafwise reduced L2 cohomology is an isomorphism which only depends on the leafwise homotopy class of the homotopy equivalence.

Keywords

foliationleafwise homotopy equivalenceisomorphismleafwise cohomology
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 3 , June 2012 , pp. 503 - 520
Copyright
Copyright © ISOPP 2011

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