Univ., Diss.--Sendai, 2000.

A proof of the Moore theorem which in the case of a principal fibration gives a spectral sequence converging to the homology of the base space is given. Also computed is the algebra structure of the homology of the Grassmannians, using Hopf algebra techniques and the cohomology of Grassmanians. Finally, it is shown that a spectral sequence for regular covering which was constructed earlier is a special case of the Moore Theorem. / Science, Faculty of / Mathematics, Department of / Graduate

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

"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

Thesis--Ph. D., University of Hong Kong.

"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

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Not available / text

A fibrewise coHopf space X over a base B is a sectioned space for which the diagonal map X —> X x _BX may be compressed into X V_BX up to fibrewise pointed homotopy. Such spaces have been investigated by I. M. James in the case where X is a sphere bundle over a sphere. The purpose of this thesis is to demonstrate some of the properties of fibrewise coHopf spaces over more general bases. Particular attention is given to sphere bundles and fibrations with spherical fibre. The fibrewise reduced suspension of a sectioned fibrewise space with closed sec- tion is fibrewise coHopf with associative comultiplication (up to fibrewise pointed homotopy) and a fibrewise inversion. Examples of fibrewise coHopf spaces not of this form are exhibited, and sufficient conditions are given to ensure that a fibrewise coHopf space has the primitive fibrewise pointed homotopy type of a fibrewise re- duced suspension, in terms of the dimension and connectivity of the space, its base and the fibres. It is shown that these conditions may be relaxed if the fibrewise coHopf structure on the space is assumed to be homotopy-associative. An example of a non-associative fibrewise coHopf sphere bundle is given. It is shown that, if q > 1 is odd, a sectioned orientable q-sphere bundle over a finite connected complex is fibrewise coHopf if and only if its fibrewise localisation at the prime 2 is fibrewise coHopf. Moreover, the fibrewise rationalisation of an odd-dimensional sphere bundle over a finite polyhedron whose fibrewise unreduced suspension is fibrewise coHopf is shown to be a trivial fibration. As an application, it is shown that new fibrewise coHopf spherical fibrations may be constructed by mixing. The Thorn space is used to determine the cohomology ring of the total space of a fibrewise coHopf sphere bundle in terms of that of its base, and a generalised Hopf invariant is constructed which vanishes on fibrewise coHopf sphere bundles.

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