Two Applications of Topological Fixed Point Theory

Chaitanya Ambi

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arXiv · 2304.09430

Two Applications of Topological Fixed Point Theory

Chaitanya Ambi

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Abstract

We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order not only fixes a point, but also maps a pencil of geodesics to itself. We apply similar techniques to the automorphism group of a smoothly bounded domain in the complex plane having connectivity three or more. We show that any prime dividing the order of this finite group must divide a certain integer depending only on the connectivity of the domain.

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Chaitanya Ambi. 2023-04-19. Two Applications of Topological Fixed Point Theory. https://arxiv.org/abs/2304.09430

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