Knots and links in lens spaces

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.

Influence of application mode of universal adhesives on bond strength performances and enzymatic activity of coronal and radicular dentin

Objective: The aims of this thesis were to analyze the application mode of the universal adhesives (UA) and to give instructions for clinical procedures. The etching mode of UA on the bond strength to dentin and on the risk of retention, marginal discoloration, marginal adaptation and post-operative sensitivity (POS) was analyzed by two systematic reviews. Three in vitro studies were conducted: 1) evaporation mode of a UA on coronal dentin; 2) cementation approach on radicular dentin; 3) adhesion of metal brackets to enamel. Materials and methods: Two systematic review were conducted firstly, then in vitro study to investigate the evaporation mode in presence or not of pulpal pressure by means of μTBS, and the enzymatic activity using in situ zymography, at T0 and T6. The cementation of a fiber into radicular dentin with different resin-cements was studied, by push-out bond strength evaluation. Orthodontic brackets were cemented according to 4 adhesive protocols and shear bond strength test was conducted. Two adhesive removal techniques were evaluated, and spectrophotometry was used. Results: The probability of POS occurrence was less in SE. SEE approach seems to perform better than SE. Air-drying resulted in higher μTBS. Suction-evaporation, aging and ER mode increased MMPs activity. Differences in NL expression were present at T0 for fiber post study, and the aging produced an increase in marginal infiltration. Brackets cemented with new universal cement with previous etchant application showed good μTBS values. Conclusion: SEE performed better than SE and TE with UA in terms of uTBS. Evaporating with air-drying is better for UA in terms of uTBS and enzymatic activity. Aging and choice of resin cement for cementation of fiber posts influenced the PBS. Brackets cementation with a new resin- cement seems to offer the highest bond strength and leaves more cement remnants after the bracket removal.