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DIFFERENTIAL FORMS ON STRATIFIED SPACES II

Part of: General theory of differentiable manifolds

Published online by Cambridge University Press:  04 January 2019

SERAP GÜRER Open the ORCID record for SERAP GÜRER [Opens in a new window]  and
PATRICK IGLESIAS-ZEMMOUR Open the ORCID record for PATRICK IGLESIAS-ZEMMOUR [Opens in a new window]
SERAP GÜRER
Affiliation:
Galatasaray University, Ortaköy, Çirağan Cd. No: 36, 34349 Beşiktaş, Istanbul, Turkey email [email protected]
PATRICK IGLESIAS-ZEMMOUR*
Affiliation:
Aix Marseille Univ., CNRS, Centrale Marseille, I2M, Marseille, France Einstein Institute of Mathematics Edmond J. Safra Campus, The Hebrew University of Jerusalem Givat Ram. Jerusalem, 9190401, Israel email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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We prove that, for conelike stratified diffeological spaces, a zero-perverse form is the restriction of a global differential form if and only if its index is equal to one for every stratum.

Keywords

stratificationdiffeologydifferential form

MSC classification

Primary: 58A35: Stratified sets
Secondary: 58A10: Differential forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 311 - 318
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

This research is partially supported by Tübitak, Career Grant No. 115F410, and the French-Turkish Research Fellowships Program, Embassy of France in Turkey 2017.

References

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Iglesias-Zemmour, P., Diffeology, Mathematical Surveys and Monographs, 185 (American Mathematical Society, Providence, RI, 2013).Google Scholar
Kloeckner, B., Quelques notions d’espaces stratifiés, Séminaire de Théorie Spectrale et Géométrie, 26 (Université de Grenoble, 1, Grenoble, 2007–2008), 13–28.Google Scholar
Pflaum, M., Analytic and Geometric Study of Stratified Spaces, Lecture notes in Mathematics, 1768 (Springer, Berlin, Heidelberg, 2001).Google Scholar
Siebenmann, L., ‘Deformation of homeomorphisms on stratified sets’, Comment. Math. Helv. 47 (1972), 123–163.Google Scholar