Thesis--Wisconsin. / Vita. Includes bibliographical references (leaf [90]).

Cyclic surgery on satellite knots in S³ is classified and a necessary condition is given for a knot in S³ to admit a nontrivial cyclic surgery with slope m/l, \m\ > 1. A complete classification of cyclic group actions on the Poincaré sphere with 1-dimensional fixed point sets is obtained. It is proved that the following knots have property I, i.e. the fundamental group of the manifold obtained by Dehn surgery on such a knot cannot be the binary icosahedral group I₁₂₀, the fundamental group of the Poincaré homology 3-sphere: nontrefoil torus knots, satellite knots, nontrefoil generalized double knots, periodic knots with some possible specific exceptions, amphicheiral strongly invertible knots, certain families of pretzel knots. Further the Poincaré sphere cannot be obtained by Dehn surgery on slice knots and a certain family of knots formed by band-connect sums. It is proved that if a nonsufficiently large hyperbolic knot in S³ admits two nontrivial cyclic Dehn surgeries then there is at least one nonintegral boundary slope for the knot. There are examples of such knots. Thus nonintegral boundary slopes exist. / Science, Faculty of / Mathematics, Department of / Graduate

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: John Luecke. Vita. Includes bibliographical references. Available also from UMI company.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1999. / Includes bibliographical references. Also available on the Internet.

Let Γ be a crystallographic group acting on the n-dimensional Euclidean space. In this dissertation, the surgery obstruction groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H_*(Rⁿ /Γ; L(p)) → L_*^-∞(Γ). / Ph. D.

This thesis is devoted to the study of the effect of Legendrian surgery on contact manifolds. In particular, we study the effect of this surgery on the Reeb dynamics of the contact manifold on which we perform such a surgery along Legendrian links. We obtain an exact sequence of cyclic Legendrian homology for the Legendrian links. Then we present the applications in 3-dimension and higher dimensions. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished