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Permuting actions, moment maps and the generalized Seiberg-Witten equations

dc.contributor.advisorPidstrygach, Viktor Prof. Dr.
dc.contributor.authorCallies, Martin
dc.date.accessioned2016-04-21T08:49:26Z
dc.date.available2016-04-21T08:49:26Z
dc.date.issued2016-04-21
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-0028-8738-7
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-5618
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510de
dc.titlePermuting actions, moment maps and the generalized Seiberg-Witten equationsde
dc.typedoctoralThesisde
dc.contributor.refereePidstrygach, Viktor Prof. Dr.
dc.date.examination2016-02-09
dc.description.abstractengIn this thesis, we study properties and the geometry related to the generalization of the Seiberg-Witten equations introduced by Taubes and Pidstrygach. A crucial ingrediant to these equations is a hyperkähler manifold M with a permuting Sp(1)-action. We study the differential forms induced on M and construct cocycles of degree 2 and 4 in the Cartan model for equivariant cohomology and the corresponding (generalizations of) moment maps in hyperkähler and multi-symplectic geometry. We generalize this and provide a natural and explicit construction of such a homotopy moment map for each cocycle in the Cartan model (of arbitrary degree). Coming back to the generalized Seiberg-Witten equations, we study properties of the generalized Dirac operator and provide new Lichnerowicz-Weitzenböck formulas in dimension 3. Finally, we give a list of examples of the generalized Seiberg-Witten equations, which have been studied in the literature.de
dc.contributor.coRefereeSchick, Thomas Prof. Dr.
dc.subject.enggeneralized Seiberg-Witten equationsde
dc.subject.engmoment mapsde
dc.subject.engn-plectic geometryde
dc.subject.engDirac operatorde
dc.subject.engpermuting actionde
dc.subject.enghyperkählerde
dc.subject.engWeitzenböck formulade
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-0028-8738-7-7
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn857342134


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