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English

Authors.
myself and Michihiro Sakai
Journal.
preprint.
Abstract.
Topological complexity of a space is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version of topological complexity with an additional condition: in a robot motion planning, a motion must be stasis if the initial and the terminal states are the same. Our main goal is to show the equalities and , where is a fibrewise pointed space over whose projection and section are given by the canonical projection to the second factor and the diagonal. In addition, our method in studying fibrewise L-S category is able to treat a fibrewise space with singular fibres.

Topological complexity is a fibrewise L-S category (adobe-pdf file, 481.1 Kbytes)