The Index of Dirac Operators on Incomplete Edge Spaces
We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a ''geometric Witt condition''. We accomplish this by cutting off to a smooth manifold with boundary, applying the Atiyah-Patodi-Singer index theorem, and taking...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
| Hauptverfasser: | , |
| 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/123456789/147856 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Index of Dirac Operators on Incomplete Edge Spaces / P. Albin, J. Gell-Redman // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 62 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862704659888603136 |
|---|---|
| author | Albin, P. Gell-Redman, J. |
| author_facet | Albin, P. Gell-Redman, J. |
| citation_txt | The Index of Dirac Operators on Incomplete Edge Spaces / P. Albin, J. Gell-Redman // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 62 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a ''geometric Witt condition''. We accomplish this by cutting off to a smooth manifold with boundary, applying the Atiyah-Patodi-Singer index theorem, and taking a limit. We deduce corollaries related to the existence of positive scalar curvature metrics on incomplete edge spaces.
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| first_indexed | 2025-12-07T16:51:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147856 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:51:35Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Albin, P. Gell-Redman, J. 2019-02-16T09:20:35Z 2019-02-16T09:20:35Z 2016 The Index of Dirac Operators on Incomplete Edge Spaces / P. Albin, J. Gell-Redman // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 62 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58G10; 58A35; 58G05 DOI:10.3842/SIGMA.2016.089 https://nasplib.isofts.kiev.ua/handle/123456789/147856 We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a ''geometric Witt condition''. We accomplish this by cutting off to a smooth manifold with boundary, applying the Atiyah-Patodi-Singer index theorem, and taking a limit. We deduce corollaries related to the existence of positive scalar curvature metrics on incomplete edge spaces. ments
 P.A. was supported by NSF grant DMS-1104533 and Simons Foundation grant #317883. The
 authors are happy to thank Rafe Mazzeo and Richard Melrose for many useful and interesting
 discussions. They are also grateful to the comments of the anonymous referees, particularly
 their suggestion of Remark 3.5. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Index of Dirac Operators on Incomplete Edge Spaces Article published earlier |
| spellingShingle | The Index of Dirac Operators on Incomplete Edge Spaces Albin, P. Gell-Redman, J. |
| title | The Index of Dirac Operators on Incomplete Edge Spaces |
| title_full | The Index of Dirac Operators on Incomplete Edge Spaces |
| title_fullStr | The Index of Dirac Operators on Incomplete Edge Spaces |
| title_full_unstemmed | The Index of Dirac Operators on Incomplete Edge Spaces |
| title_short | The Index of Dirac Operators on Incomplete Edge Spaces |
| title_sort | index of dirac operators on incomplete edge spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147856 |
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