Relative topology, motion planning, and coverage problems

Abstract: Algebraic topology produces invariants that capture aspects of the shape of a space, or in the case of topological data analysis. Although these invariants are in general quite rich, they are somewhat sparse in low dimensions. On the other hand, it is possible to consider comma categories of spaces, for example the category of spaces with reference to a fixed base space and morphisms respecting the reference map. When one does this, one obtains a much richer set of invariants. I will discuss how to apply this kind of construction in the setting of evasion problems for sensor nets and more general motion planning problems.

Computer sciencealgebraic topologycategory theorylogic

Audience: learners

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Topos Institute Colloquium