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dc.contributor.authorSuan, Caleb 21:41:32 (GMT) 21:41:32 (GMT)
dc.description.abstractIn this thesis, we study differential operators on manifolds with torsion-free G2-structure. In particular, we use an identification of the spinor bundle S of such a manifold M with the bundle R ⊕ T*M to reframe statements regarding the Dirac operator in terms of three other first order differential operators: the divergence, the gradient, and the curl operators. We extend these three operators to act on tensors of one degree higher and study the properties of the extended operators. We use the extended operators to describe a Dirac bundle structure on the bundle T*M ⊕ (T*M ⊗ T*M) = T*M ⊗ (R ⊕ T*M) as well as its Dirac operator. We show that this Dirac operator is equivalent to the twisted Dirac operator DT defined using the original identification of S with R ⊕ T*M. As the two Dirac operators are equivalent, we use the T*M ⊕ (T*M ⊗ T*M) = T*M ⊗ (R ⊕ T*M) description of the bundle of spinor-valued 1-forms to examine the properties of the twisted Dirac operator DT. Using the extended divergence, gradient, and curl operators, we study the kernel of the twisted Dirac operator when M is compact and provide a proof that dim (ker DT) = b2 + b3.en
dc.publisherUniversity of Waterlooen
dc.subjectdifferential geometryen
dc.subjecttwisted Dirac operatoren
dc.subjectdifferential operatorsen
dc.titleDifferential Operators on Manifolds with G2-Structureen
dc.typeMaster Thesisen
dc.pendingfalse Mathematicsen Mathematicsen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorKarigiannis, Spiro
uws.contributor.affiliation1Faculty of Mathematicsen

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