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Article: On the instanton complex of holomorphic morse theory
Title | On the instanton complex of holomorphic morse theory |
---|---|
Authors | |
Issue Date | 2003 |
Publisher | International Press. The Journal's web site is located at http://www.intlpress.com |
Citation | Communications In Analysis And Geometry, 2003, v. 11 n. 4, p. 775-807 How to Cite? |
Abstract | Consider a holomorphic torus action on a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set form a partially ordered set, we construct, using sheaf-theoretical techniques, two spectral sequences that converges to the twisted Dolbeault cohomology groups and those with compact support, respectively. These spectral sequences are the holomorphic counterparts of the instanton complex in standard Morse theory. The results proved imply holomorphic Morse inequalities and fixed-point formulas on a possibly non-compact manifold. Finally, examples and applications are given. |
Persistent Identifier | http://hdl.handle.net/10722/156207 |
ISSN | 2023 Impact Factor: 0.7 2023 SCImago Journal Rankings: 0.961 |
References |
DC Field | Value | Language |
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dc.contributor.author | Wu, S | en_US |
dc.date.accessioned | 2012-08-08T08:40:50Z | - |
dc.date.available | 2012-08-08T08:40:50Z | - |
dc.date.issued | 2003 | en_US |
dc.identifier.citation | Communications In Analysis And Geometry, 2003, v. 11 n. 4, p. 775-807 | en_US |
dc.identifier.issn | 1019-8385 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156207 | - |
dc.description.abstract | Consider a holomorphic torus action on a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set form a partially ordered set, we construct, using sheaf-theoretical techniques, two spectral sequences that converges to the twisted Dolbeault cohomology groups and those with compact support, respectively. These spectral sequences are the holomorphic counterparts of the instanton complex in standard Morse theory. The results proved imply holomorphic Morse inequalities and fixed-point formulas on a possibly non-compact manifold. Finally, examples and applications are given. | en_US |
dc.language | eng | en_US |
dc.publisher | International Press. The Journal's web site is located at http://www.intlpress.com | en_US |
dc.relation.ispartof | Communications in Analysis and Geometry | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | On the instanton complex of holomorphic morse theory | en_US |
dc.type | Article | en_US |
dc.identifier.email | Wu, S:swu@maths.hku.hk | en_US |
dc.identifier.authority | Wu, S=rp00814 | en_US |
dc.description.nature | preprint | en_US |
dc.identifier.scopus | eid_2-s2.0-4043181903 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-4043181903&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 11 | en_US |
dc.identifier.issue | 4 | en_US |
dc.identifier.spage | 775 | en_US |
dc.identifier.epage | 807 | en_US |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Wu, S=15830510400 | en_US |
dc.identifier.issnl | 1019-8385 | - |