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Full-Text Articles in Mathematics
Classification Of Spacetimes With Symmetry, Jesse W. Hicks
Classification Of Spacetimes With Symmetry, Jesse W. Hicks
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we
i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes;
ii) create digital databases of the classification for easy access and use for researchers;
iii) create software to classify any spacetime metric with symmetry against the new database;
iv) compare results of our …
The Fundamental Groups Of The Complements Of Some Solid Horned Spheres, Norman William Riebe
The Fundamental Groups Of The Complements Of Some Solid Horned Spheres, Norman William Riebe
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
One of the methods used for the construction of the classical Alexander horned sphere leads naturally to generalization to horned spheres of higher order. Let M2, denote the Alexander horned sphere. This is a 2-horned sphere of order 2. Denote by M3 and M4, two 2-horned spheres of orders 3 and 4, respectively, constructed by such a generalization.
The fundamental groups of the complements of M2, M3, and M4 are derived, and representations of these groups onto the Alternating Group, A5, are found. The form of the presentations …