Higher topological complexity of subcomplexes of products of spheres and related polyhedral product spaces
DOI: http://dx.doi.org/10.12775/TMNA.2016.051
Abstract
We construct ``higher'' motion planners for automated systems
whose spaces of states are homotopy equivalent to a polyhedral
product space $Z(K,\{(S^{k_i},\star)\})$, {e.g. robot arms with
restrictions on the possible combinations of simultaneously moving
nodes.} Our construction is shown to be optimal by explicit
cohomology calculations. The higher topological complexity of
other {families of} polyhedral product spaces is also determined.
whose spaces of states are homotopy equivalent to a polyhedral
product space $Z(K,\{(S^{k_i},\star)\})$, {e.g. robot arms with
restrictions on the possible combinations of simultaneously moving
nodes.} Our construction is shown to be optimal by explicit
cohomology calculations. The higher topological complexity of
other {families of} polyhedral product spaces is also determined.
Keywords
Sequential motion planning; Schwarz genus; polyhedral products; zero-divisors
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