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arXiv · 1911.12522

Farley-Sabalka's Morse-theory model and the higher topological complexity of ordered configuration spaces on trees

Jorge Aguilar-Guzmán·Jesús González·Teresa Hoekstra-Mendoza
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Abstract

Using the ordered analogue of Farley-Sabalka's discrete gradient field on the configuration space of a graph, we unravel a levelwise behavior of the generators of the pure braid group on a tree. This allows us to generalize Farber's equivariant description of the homotopy type of the configuration space on a tree on two particles. The results are applied to the calculation of all the higher topological complexities of ordered configuration spaces on trees on any number of particles.

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Jorge Aguilar-Guzmán, Jesús González, Teresa Hoekstra-Mendoza. 2019-11-28. Farley-Sabalka's Morse-theory model and the higher topological complexity of ordered configuration spaces on trees. https://arxiv.org/abs/1911.12522

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