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This article is cited in 4 scientific papers (total in 4 papers)
Dolbeault Complex on $S^4\setminus \{\,\cdot\,\}$ and $S^6\setminus\{\,\cdot\,\}$ through Supersymmetric Glasses
Andrei V. Smilga SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France
Abstract:
$S^4$ 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 $\partial$ 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 $S^4\setminus\{\,\cdot\,\}$ is equal to $3$.
Keywords:
Dolbeault, supersymmetry.
Received: June 22, 2011; in final form November 9, 2011; Published online November 15, 2011
Citation:
Andrei V. Smilga, “Dolbeault Complex on $S^4\setminus \{\,\cdot\,\}$ and $S^6\setminus\{\,\cdot\,\}$ through Supersymmetric Glasses”, SIGMA, 7 (2011), 105, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma663 https://www.mathnet.ru/eng/sigma/v7/p105
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Abstract page: | 160 | Full-text PDF : | 46 | References: | 34 |
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