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dc.contributor.authorHerman, Jonathan 14:53:46 (GMT) 14:53:46 (GMT)
dc.description.abstractWe introduce the notion of a weak (homotopy) moment map associated to a Lie group action on a multisymplectic manifold. We show that the existence/uniqueness theory governing these maps is a direct generalization from symplectic geometry. We use weak moment maps to extend Noether's theorem from Hamiltonian mechanics by exhibiting a correspondence between multisymplectic conserved quantities and continuous symmetries on a multi-Hamiltonian system. We nd that a weak moment map interacts with this correspondence in a way analogous to the moment map in symplectic geometry. We de ne a multisymplectic analog of the classical momentum and position functions on the phase space of a physical system by introducing momentum and position forms. We show that these di erential forms satisfy generalized Poisson bracket relations extending the classical bracket relations from Hamiltonian mechanics. We also apply our theory to derive some identities on manifolds with a torsion-free G2 structure.en
dc.publisherUniversity of Waterlooen
dc.titleWeak Moment Maps in Multisymplectic Geometryen
dc.typeDoctoral Thesisen
dc.pendingfalse Mathematicsen Mathematicsen of Waterlooen
uws-etd.degreeDoctor of Philosophyen
uws.contributor.advisorKarigiannis, Spiro
uws.contributor.advisorHu, Shengda
uws.contributor.affiliation1Faculty of Mathematicsen

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