Motion planning in connected sums of real projective spaces

Abstract

The topological complexity $\mathsf{TC}(X)$ is a homotopy invariant of a topological space $X$, motivated by robotics, and providing a measure of the navigational complexity of $X$. The topological complexity of a connected sum of real projective planes, that is, a high genus nonorientable surface, is known to be maximal. We use algebraic tools to show that the analogous result holds for connected sums of higher dimensional real projective spaces.

10 pages

Cited by in corpus (2)

• Sequential motion planning in connected sums of real projective spaces
• Sequential motion planning assisted by group actions