On higher analogs of topological complexity

Details On higher analogs of topological complexity On higher analogs of topological complexity

2009-09-09

arxiv.org/abs/0909.1616v3

Mathematics

Algebraic Topology

LATEX, 8 pages

Scientific paper

Farber introduced a notion of topological complexity $\TC(X)$ that is related
to robotics. Here we introduce a series of numerical invariants $\TC_n(X),
n=1,2, ...$ such that $\TC_2(X)=\TC(X)$ and $\TC_n(X)\le \TC_{n+1}(X)$. For
these higher complexities, we define their symmetric versions that can also be
regarded as higher analogs of the symmetric topological complexity.

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