Topological Complexities of Surfaces

2014/02/01 by Ibai Basabe, Basabe, Ibai
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT

paper · pdf · doi:10.48550/arxiv.1402.0044

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arxiv created 2019/02/28 · arxiv updated 2019/03/01

Abstract

The sphere S² and the torus T² are the only closed connected surfaces for which higher topological complexities are known (for each n∈\2,3,...\⊂ℕ, TC_n(S²)=n and TC_n(T²)=2n-2). This text aims to find topological complexities for most other closed connected surfaces. For all but S², T², the projective plane (ℝℙ²) and the Klein bottle the n-th topological complexity is 2n.

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