On higher analogs of topological complexity

By Yuli B. Rudyak. 2009

138 citations recorded by the source corpus.

Abstract Farber introduced a notion of topological complexity TC ( X ) that is related to robotics. Here we introduce a series of numerical invariants TC n ( X ) , n = 2 , 3 , …  , such that TC 2 ( X ) = TC ( X ) and TC n ( X ) ⩽ TC n + 1 ( X ) . For these higher complexities, we define their symmetric versions that can also be regarded as higher analogs of the symmetric topological complexity.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a834fcc5929e78379ffd8ed512c00ba416de9df7

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In Computational Theory and Mathematics

1. Yuli B. Rudyak
2. Jesús González
3. D. Tamaki
4. I. Basabe

In Mathematical Physics

1. Yuli B. Rudyak
2. Jesús González
3. D. Tamaki
4. I. Basabe

Citations in the corpus

• Higher topological complexity and its symmetrization (2010, background): “X /, the nth topological complexity of X , introduced by the third author in [23] and reviewed in Section 2 (where we use normalized notation, ie in such a way that contractible spaces have TCn D 0).”