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.

Ruolo dei glicosaminoglicani su struttura e funzione dei crimps nei tendini e nei legamenti

The biomechanical roles of both tendons and ligaments are fulfilled by extracellular matrix of these tissues. In particular, tension is mainly transmitted and resisted by fibrous proteins (collagen, elastin), whereas compressive load is absorbed by water-soluble glycosaminoglycans (GAGs). GAGs spanning the interfibrillar spaces and interacting with fibrils also seem to play a part in transmitting and resisting tensile stresses. Apart from different functional roles and collagen array, tendons and ligaments share the same basic structure showing periodic undulations of collagen fibers or crimps. Each crimp is composed of many knots of each single fibril or fibrillar crimps. Fibrillar and fiber crimps act as shock absorbers during the initial elongation of both tendons and ligaments and assist the elastic recoil of fibrils and fibers when the tensile stress is removed. The aim of this thesis was to evaluate whether GAGs directly affect the 3D microstructural integrity of fibrillar crimp and fiber crimps in both tendons and ligaments. Achilles tendons and medial collateral ligaments of the knee from eight female Sprague-Dawley rats (90 days old) were digested with chondroitinase ABC to remove GAGs and observed under a scanning electron microscope (SEM). In addition, isolated fibrils from these tissues obtained by mechanical homogenization were analyzed by a transmission electron microscope (TEM). Both samples digested with chondroitinase ABC or mechanically disrupted still showed crimps and fibrillar crimps comparable to tissues with a normal GAGs content. All fibrils in the fibrillar crimp region always twisted leftwards, thus changing their running plane, and then sharply bent, changing their course on a new plane. These data suggest that GAGs do not affect structural integrity or fibrillar crimps functions that seem mainly related to the local fibril leftward twisting and the alternating handedness of collagen from a molecular to a supramolecular level.

La resistenza dei legami. Narrazioni e rappresentazioni della famiglia nella trilogia di romanzi “Past Imperfect” (2004-2011) di Nuruddin Farah

Il presente progetto di ricerca riguarda la terza trilogia di romanzi di Nuruddin Farah, “Past Imperfect” (2004-2011). L’analisi dei tre testi che compongono la trilogia – “Links” (2004), “Knots” (2007) e “Crossbones” (2011) – evidenzia la persistente rilevanza delle narrazioni e delle rappresentazioni della famiglia all’interno di tutta la produzione letteraria dell’autore. Questa prospettiva critica richiede l’impiego di una metodologia che riunisce vari aspetti della critica letteraria di matrice post-strutturalista e, per altri versi, di stampo materialista, assecondando così le due principali tendenze critiche presenti all’interno degli studi postcoloniali. Lo stesso approccio teorico-metodologico può essere applicato anche in altri due ambiti critici chiamati in causa dalla trilogia di Nuruddin Farah: la cosiddetta “world literature” e la cosiddetta “failed-state fiction”. L’analisi delle narrazioni e delle rappresentazioni della famiglia richiede, inoltre, un approccio interdisciplinare molto esteso, stimolando ricerche negli ambiti della semiotica, dell’antropologia, della psicanalisi, dei Gender Studies e dei Trauma Studies.

A hydrodynamical view on the mass accretion onto massive halos

This Thesis presents the results of my work on how galaxy clusters form by the accretion of sub-clumps and diffuse materials, and how the accreted energy is distributed in the X-ray emitting plasma. Indeed, on scales larger than tens of millions of light years, the Universe is self-organised by gravity into a spiderweb, the Cosmic Web. Galaxy clusters are the knots of this Cosmic Web, but a strong definition of filaments (which link different knots) and their physical proprieties, is still uncertain. Even if this pattern was determined by studying the spatial distribution of galaxies in the optical band, recently, also in the X-rays probes of filamentary structures around galaxy clusters were obtained. Therefore, given these observational facilities, the galaxy clusters’ outskirts are the best candidate regions to detect filaments and study their physical characteristics. However, from X-rays observations, we have only a few detections of cosmic filaments to date. On the other hand, it is crucial to understand how the accreted energy is dissipated in the baryon content of galaxy clusters and groups. Indeed, it is well known that in the central region of galaxy clusters and groups, the baryon fraction increases with the halo mass. On the outer region, the lack of X-rays constraints influences our understanding of the evolution of baryons in the halos volume. The standard assumption of “closed-box” system, for which the baryon fraction should approach the cosmological ratio Omega_bar/Omega_m, for galaxy clusters and groups seems to be too strong, especially for less massive objects. Moreover, a complete redshift evolution of baryons in galaxy clusters and groups is still missing.