Speech and narrative: characterisation techniques in the "Aeneid"

The thesis provides a comprehensive analysis of the characterisation of two of the major figures in the Aeneid, Aeneas and Turnus. Particular attention is paid to their direct speeches, all of which are examined and, where relevant, compared to Homeric models and parallels. To this purpose considerable use is made of the indices in Knauer's Die Aeneis und Homer. A more general comparison is made between the dramatic (direct speech) role of Aeneas and those of Homer's Achilles (Iliad) and Odysseus (Odyssey). An appraisal is made (from the viewpoint of depiction of character) of the relationship between the direct and indirect speeches in the Aeneid. Reasons are given to suggest that it is not mere chance, or for the sake of variety, that certain speeches of Aeneas and Turnus are expressed in oratio obliqua. In addition, the narrative portrayal of Aeneas and Turnus is considered in apposition to that of the speeches. A distinction is drawn between Vergil's direct method of characterisation (direct speeches) and his indirect methods (narrative/oratio obliqua). Inevitably, the analysis involves major consideration of the Roman values which pervade the work. All speeches, thoughts and actions of Aeneas and Turnus are assessed in terms of pietas, impietas, furor, virtus, ratio, clementia, humanitas (etc.). It is shown that individual concepts (such as pietas and impietas) are reflected in Vergil's direct and indirect methods of characterisation. The workings of fate and their relevance to the pietas concept are discussed throughout.

Alternating surgeries

This thesis is concerned with the question of when the double branched cover of an alternating knot can arise by Dehn surgery on a knot in S^3. We approach this problem using a surgery obstruction, first developed by Greene, which combines Donaldson's Diagonalization Theorem with the $d$-invariants of Ozsvath and Szabo's Heegaard Floer homology. This obstruction shows that if the double branched cover of an alternating knot or link L arises by surgery on S^3, then for any alternating diagram the lattice associated to the Goeritz matrix takes the form of a changemaker lattice. By analyzing the structure of changemaker lattices, we show that the double branched cover of L arises by non-integer surgery on S^3 if and only if L has an alternating diagram which can be obtained by rational tangle replacement on an almost-alternating diagram of the unknot. When one considers half-integer surgery the resulting tangle replacement is simply a crossing change. This allows us to show that an alternating knot has unknotting number one if and only if it has an unknotting crossing in every alternating diagram. These techniques also produce several other interesting results: they have applications to characterizing slopes of torus knots; they produce a new proof for a theorem of Tsukamoto on the structure of almost-alternating diagrams of the unknot; and they provide several bounds on surgeries producing the double branched covers of alternating knots which are direct generalizations of results previously known for lens space surgeries. Here, a rational number p/q is said to be characterizing slope for K in S^3 if the oriented homeomorphism type of the manifold obtained by p/q-surgery on K determines K uniquely. The thesis begins with an exposition of the changemaker surgery obstruction, giving an amalgamation of results due to Gibbons, Greene and the author. It then gives background material on alternating knots and changemaker lattices. The latter part of the thesis is then taken up with the applications of this theory.