The topological complexity sequence of any group with infinite cohomological dimension is weakly increasing and unbounded, with growth estimates and exact asymptotics determined for finite groups of even order.
Distributional topological complexity of groups.Preprint
4 Pith papers cite this work. Polarity classification is still indexing.
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Proves dTC(Γ)=TC(Γ) for torsion-free hyperbolic and nilpotent groups, shows dTC(L^n_p)≤2p-1 and dcat(L^n_p)≤p-1 (equality in some cases), and derives counterexamples to product formulas.
Defines a new probabilistic lower-bound invariant for parametrized topological complexity and proves it matches classical behavior on Fadell-Neuwirth fibrations and sphere bundles but differs on real projective space bundles with SO structure groups.
Analog category of a finite group is essentially proportional to the order of its largest Sylow subgroup, rendering the group-order upper bound far from optimal.
citing papers explorer
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Topological complexity sequences of groups
The topological complexity sequence of any group with infinite cohomological dimension is weakly increasing and unbounded, with growth estimates and exact asymptotics determined for finite groups of even order.
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On distributional topological complexity of groups and manifolds
Proves dTC(Γ)=TC(Γ) for torsion-free hyperbolic and nilpotent groups, shows dTC(L^n_p)≤2p-1 and dcat(L^n_p)≤p-1 (equality in some cases), and derives counterexamples to product formulas.
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On the complexity of parametrized motion planning algorithms
Defines a new probabilistic lower-bound invariant for parametrized topological complexity and proves it matches classical behavior on Fadell-Neuwirth fibrations and sphere bundles but differs on real projective space bundles with SO structure groups.
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On the analog category of finite groups
Analog category of a finite group is essentially proportional to the order of its largest Sylow subgroup, rendering the group-order upper bound far from optimal.