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Torelli Actions and Smooth Structures on 4-manifolds

dc.contributor.advisorWinkelnkemper, Horst Een_US
dc.contributor.authorCalcut, Jack Samuelen_US
dc.description.abstractIn the theory of Artin presentations, a smooth four manifold is already determined by an Artin presentation of the fundamental group of its boundary. Thus, one of the central problems in four dimensional smooth topology, namely the study of smooth structures on these manifolds and their Donaldson and Seiberg-Witten invariants, can be approached in an entirely new, exterior, purely group theoretic manner. The main purpose of this thesis is to explicitly demonstrate how to change the smooth structure in this manner. These examples also have physical relevance. We also solve some related problems. Namely, we study knot and link theory in Artin presentation theory, give a group theoretic formula for the Casson invariant, study the combinatorial group theory of Artin presentations, and state some important open problems.en_US
dc.format.extent523112 bytes
dc.titleTorelli Actions and Smooth Structures on 4-manifoldsen_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.subject.pquncontrolledArtin Presentationen_US
dc.subject.pquncontrolledTorelli actionen_US
dc.subject.pquncontrolledthree manifolden_US
dc.subject.pquncontrolledfour manifolden_US

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