Norio Iwase
Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp
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  = cat^{*}_{B}(d(B))+1)
and  = cat^{B}_{B}(d(B))+1)
, where =B{\times}B)
is a fibrewise pointed space over whose projection and section are given by }=pr_{2} : B{\times}B \to B)
the canonical projection to the second factor and }=\Delta_{B} : B \to B{\times}B)
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)