Motion planning in connected sums of real projective spaces

Daniel C. Cohen; Lucile Vandembroucq

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arXiv · 1807.09947

Motion planning in connected sums of real projective spaces

Daniel C. Cohen·Lucile Vandembroucq

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Abstract

The topological complexity ${\sf TC}(X)$ 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.

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Daniel C. Cohen, Lucile Vandembroucq. 2018-07-26. Motion planning in connected sums of real projective spaces. https://arxiv.org/abs/1807.09947

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