Browsing by Author "Oprea, John"
Now showing items 1-3 of 3
-
Bredon Cohomology and Robot Motion Planning
[OWP-2017-34] Farber, Michael; Grant, Mark; Lupton, Gregory; Oprea, John (Mathematisches Forschungsinstitut Oberwolfach, 2017-11-29)In this paper we study the topological invariant TC(X) reflecting the complexity of algorithms for autonomous robot motion. Here, X stands for the configuration space of a system and TC(X) is, roughly, ... -
Hight functions on quaternionic Stiefel manifolds
[OWP-2015-10] Macías-Virgós, Enrique; Strom, Jeffrey; Tanré, Daniel; Oprea, John (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)In this note, we study height functions on quaternionic Stiefel manifolds and prove that all these height functions are Morse-Bott. Among them, we characterize the Morse functions and give a lower bound for their number ... -
Topological Complexity, Robotics and Social Choice
[SNAP-2018-005-EN] Carrasquel, José; Lupton, Gregory; Oprea, John (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-10)Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the ...