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Article: On the instanton complex of holomorphic morse theory

TitleOn the instanton complex of holomorphic morse theory
Authors
Issue Date2003
PublisherInternational 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?
AbstractConsider 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 Identifierhttp://hdl.handle.net/10722/156207
ISSN
2015 Impact Factor: 0.623
2015 SCImago Journal Rankings: 1.692
References

 

DC FieldValueLanguage
dc.contributor.authorWu, Sen_US
dc.date.accessioned2012-08-08T08:40:50Z-
dc.date.available2012-08-08T08:40:50Z-
dc.date.issued2003en_US
dc.identifier.citationCommunications In Analysis And Geometry, 2003, v. 11 n. 4, p. 775-807en_US
dc.identifier.issn1019-8385en_US
dc.identifier.urihttp://hdl.handle.net/10722/156207-
dc.description.abstractConsider 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.languageengen_US
dc.publisherInternational Press. The Journal's web site is located at http://www.intlpress.comen_US
dc.relation.ispartofCommunications in Analysis and Geometryen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleOn the instanton complex of holomorphic morse theoryen_US
dc.typeArticleen_US
dc.identifier.emailWu, S:swu@maths.hku.hken_US
dc.identifier.authorityWu, S=rp00814en_US
dc.description.naturepreprinten_US
dc.identifier.scopuseid_2-s2.0-4043181903en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-4043181903&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume11en_US
dc.identifier.issue4en_US
dc.identifier.spage775en_US
dc.identifier.epage807en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridWu, S=15830510400en_US

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