Basic Forms and Orbit Spaces: a Diffeological Approach
If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper,...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147723 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Basic Forms and Orbit Spaces: a Diffeological Approach / Y. Karshon, J. Watts // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748813215662080 |
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| author | Karshon, Y. Watts, J. |
| author_facet | Karshon, Y. Watts, J. |
| citation_txt | Basic Forms and Orbit Spaces: a Diffeological Approach / Y. Karshon, J. Watts // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense.
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| first_indexed | 2025-12-07T20:56:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147723 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:56:56Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Karshon, Y. Watts, J. 2019-02-15T18:43:13Z 2019-02-15T18:43:13Z 2016 Basic Forms and Orbit Spaces: a Diffeological Approach / Y. Karshon, J. Watts // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58D19; 57R99 DOI:10.3842/SIGMA.2016.026 https://nasplib.isofts.kiev.ua/handle/123456789/147723 If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense. This work is partially supported by the Natural Sciences and Engineering Council of Canada. We
 are grateful to Patrick Iglesias-Zemmour for instructing us on dif feology and to Reyer Sjamaar
 for his inspiration, as well as to the anonymous referees for excellent suggestions that lead to
 a better organisation of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Basic Forms and Orbit Spaces: a Diffeological Approach Article published earlier |
| spellingShingle | Basic Forms and Orbit Spaces: a Diffeological Approach Karshon, Y. Watts, J. |
| title | Basic Forms and Orbit Spaces: a Diffeological Approach |
| title_full | Basic Forms and Orbit Spaces: a Diffeological Approach |
| title_fullStr | Basic Forms and Orbit Spaces: a Diffeological Approach |
| title_full_unstemmed | Basic Forms and Orbit Spaces: a Diffeological Approach |
| title_short | Basic Forms and Orbit Spaces: a Diffeological Approach |
| title_sort | basic forms and orbit spaces: a diffeological approach |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147723 |
| work_keys_str_mv | AT karshony basicformsandorbitspacesadiffeologicalapproach AT wattsj basicformsandorbitspacesadiffeologicalapproach |