"19 July 2002." / Bibliography: leaves 135-137. / viii, 137 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis develops the theory of bundle gerbes and examines and number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 2003

Let <i>G</i> be any compact connected Lie group and let <i>T</i> ≤ <i>G</i> be a maximal torus.  Then for any unstable Adams operation <i>f</i> of degree <i>k</i>, the following diagram commutes up to homotopy «!» And conversely, any map <i>f</i> that makes the above diagram commute must be an unstable Adams operation. Using this characterization, we will construct a self-map of a <i>p</i>-local compact group (<i>S,F,L</i>) in order to define unstable Adams operations on a more general setting. THEOREM.  For any <i>p</i>-local compact group (<i>S,F,L</i>) there is a self-equivalence such that the map on the objects when restricted to the identity component of <i>S</i> is a <i>q^m-th </i>power map.

This thesis looks into the holonomy algebras of Tractor/Cartan connections for both projective and conformal structures. Using a splitting formula and a cone construction in the Einstein case, it classifies all reductive, non-irreducible holonomy groups for conformal structures (thus fully solving the question in the definite signature case). The thesis then analyses the geometric consequences of of holonomy reduction for the projective Tractor connection. A general, Ricci-flat, cone construction pertains in the projective case, and this thesis fully classifies the irreducibly acting holonomy algebras by analysing which holonomy families admit a torsion-free Ricci-flat affine connection, and constructing cones with these properties.

"19 July 2002." / Bibliography: leaves 135-137. / viii, 137 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis develops the theory of bundle gerbes and examines and number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 2003

No description available.

We develop some basic homological theory of hopfological algebra as defined by Khovanov. A simplicial bar resolution for an arbitrary hopfological module is constructed, and some derived analogue of Morita theory is established. We also discuss about some special classes of examples that appear naturally in categorification.

Over the last twenty years, a main focus of low-dimensional topology has been on categorified knot invariants such as knot homologies. This dissertation studies the case of two such homologies under the iteration of branched covering maps. In the first part, we find a spectral sequence on the sutured annular Khovanov homology of periodic links of period $r=2^i$. In the second part, we study the asymptotic growth rate of Heegaard Floer homology of cyclic branched covers of a knot as the branching number increases.

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves 41-42).

Thesis (Ph. D.)--University of Oregon, 1999. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 103-105). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9947969.

Typescript. Includes vita and abstract. Includes bibliographical references (leaves 53-54) Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.