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The Projective Group as a Topological Manifold

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Document pages: 8 pages

Abstract: In this article, we start by a review of the circle group  [1] and its topology induced [1] by the quotient metric, which we later use to define a topological structure on the unit circle . Using points on  under the complex exponential map, we can construct orthogonal projection operators. We will show that under this construction, we arrive at a topological group, denoted  of projection matrices. Together with the induced topology, it will be demonstrated that  is Hausdorff and Second Countable forming a topological manifold. Moreover, I will use an example of a group action on  to generate subgroups of .

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