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- W2904749565 abstract "In this paper, we examine how topological complexity, simplicial complexity, discrete topological complexity, and combinatorial complexity compare when applied to models of $S^1$. We prove that the topological complexity of non-minimal finite models of $S^1$ can be less-than-or-equal-to 3, and that the TC of the minimal finite model of any $n$-sphere is equal to 4 for $n geq 1$. We show the former using properties of the LS-category, and we show the latter by proving that the TC of the non-Hausdorff suspension of any finite connected $T_0$ space is equal to 4. We also prove a result about the topological complexity of non-Hausdorff joins of discrete finite spaces, allowing us to exhibit spaces weakly homotopy equivalent to a wedge of circles with arbitrarily high TC." @default.
- W2904749565 created "2018-12-22" @default.
- W2904749565 creator A5054262136 @default.
- W2904749565 date "2018-12-18" @default.
- W2904749565 modified "2023-09-27" @default.
- W2904749565 title "The Topological Complexity of Finite Models of Spheres" @default.
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