Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses
S⁴ is not a complex manifold, but it is sufficient to remove one point to make it complex. Using supersymmetry methods, we show that the Dolbeault complex (involving the holomorphic exterior derivative ∂ and its Hermitian conjugate) can be perfectly well defined in this case. We calculate the spectr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147990 |
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| Zitieren: | Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses / A.V. Smilga // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-147990 |
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Smilga, A.V. 2019-02-16T12:45:52Z 2019-02-16T12:45:52Z 2011 Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses / A.V. Smilga // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 32C15; 53B35; 53Z05 http://dx.doi.org/10.3842/SIGMA.2011.105 https://nasplib.isofts.kiev.ua/handle/123456789/147990 S⁴ is not a complex manifold, but it is sufficient to remove one point to make it complex. Using supersymmetry methods, we show that the Dolbeault complex (involving the holomorphic exterior derivative ∂ and its Hermitian conjugate) can be perfectly well defined in this case. We calculate the spectrum of the Dolbeault Laplacian. It involves 3 bosonic zero modes such that the Dolbeault index on S⁴\{·} is equal to 3. I am indebted to G. Carron, E. Ivanov, and V. Roubtsov for useful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| spellingShingle |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses Smilga, A.V. |
| title_short |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_full |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_fullStr |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_full_unstemmed |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses |
| title_sort |
dolbeault complex on s⁴\{·} and s⁶\{·} through supersymmetric glasses |
| author |
Smilga, A.V. |
| author_facet |
Smilga, A.V. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
S⁴ is not a complex manifold, but it is sufficient to remove one point to make it complex. Using supersymmetry methods, we show that the Dolbeault complex (involving the holomorphic exterior derivative ∂ and its Hermitian conjugate) can be perfectly well defined in this case. We calculate the spectrum of the Dolbeault Laplacian. It involves 3 bosonic zero modes such that the Dolbeault index on S⁴\{·} is equal to 3.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147990 |
| citation_txt |
Dolbeault Complex on S⁴\{·} and S⁶\{·} through Supersymmetric Glasses / A.V. Smilga // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
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AT smilgaav dolbeaultcomplexons4ands6throughsupersymmetricglasses |
| first_indexed |
2025-12-07T13:25:53Z |
| last_indexed |
2025-12-07T13:25:53Z |
| _version_ |
1850856128985956352 |