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DIFFERENTIAL FORMS ON STRATIFIED SPACES

Part of: General theory of differentiable manifolds

Published online by Cambridge University Press:  13 July 2018

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, Çiraǧan Cd. No. 36, 34349 Beşktaş/İstanbul, Turkey email sgurer@gsu.edu.tr
PATRICK IGLESIAS-ZEMMOUR
Affiliation:
I2M CNRS, Marseille, France The Hebrew University of Jerusalem, Israel email piz@math.huji.ac.il
*
✉serapgurer@gmail.com
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Abstract

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First, we extend the notion of stratified spaces to diffeology. Then we characterise the subspace of stratified differential forms, or zero-perverse forms in the sense of Goresky–MacPherson, which can be extended smoothly into differential forms on the whole space. For that we introduce an index which outlines the behaviour of the perverse forms on the neighbourhood of the singular strata.

Keywords

stratificationdiffeologydifferential forms

MSC classification

Primary: 58A35: Stratified sets
Secondary: 58A10: Differential forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 319 - 330
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This research is partially supported by Tübi̇tak, Career Grant No. 115F410, Galatasaray University Research Fund Grant No. 15.504.001 and a 2017 grant of the French Embassy in Ankara, Turkey.

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