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University of Glasgow

1. Evington, Samuel. W*-Bundles.

Degree: PhD, 2018, University of Glasgow

This thesis collates, extends and applies the abstract theory of W*-bundles. Highlights include the standard form for W*-bundles, a bicommutant theorem for W*-bundles, and an investigation of completions, ideals, and quotients of W*-bundles. The Triviality Problem, whether all W*-bundles with fibres isomorphic to the hyperfinite II_1 factor are trivial, is central to this thesis. Ozawa's Triviality Theorem is presented, and property gamma and the McDuff property for W*-bundles are investigated thoroughly. Ozawa's Triviality Theorem is applied to some new examples such as the strict closures of Villadsen algebras and non-trivial C(X)-algebras. The solution to the Triviality Problem in the locally trivial case, obtained by myself and Pennig, is included. A theory of sub-W*-bundles is developed along the lines of Jones' subfactor theory. A sub-W*-bundle encapsulates a tracially continuous family of subfactors in a single object. The basic construction and the Jones tower are generalised to this new setting and the first examples of sub-W*-bundles are constructed.

Subjects/Keywords: QA Mathematics

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APA (6th Edition):

Evington, S. (2018). W*-Bundles. (Doctoral Dissertation). University of Glasgow. Retrieved from http://theses.gla.ac.uk/8650/

Chicago Manual of Style (16th Edition):

Evington, Samuel. “W*-Bundles.” 2018. Doctoral Dissertation, University of Glasgow. Accessed December 18, 2018. http://theses.gla.ac.uk/8650/.

MLA Handbook (7th Edition):

Evington, Samuel. “W*-Bundles.” 2018. Web. 18 Dec 2018.

Vancouver:

Evington S. W*-Bundles. [Internet] [Doctoral dissertation]. University of Glasgow; 2018. [cited 2018 Dec 18]. Available from: http://theses.gla.ac.uk/8650/.

Council of Science Editors:

Evington S. W*-Bundles. [Doctoral Dissertation]. University of Glasgow; 2018. Available from: http://theses.gla.ac.uk/8650/

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