Abstract: We aim to link two well-known theories; namely the string topology (founded by Chas and Sullivan in [1]) and the topological robotics (founded by Farber some few years later, in [4]). For our purpose, we consider a compact Lie group G acting on a path connected n‑manifold M. On the set of the loop motion planning algorithms, we define a string loop motion planning product and extend it to a kind of a string loop motion planning product, which endows the shifted homology with a structure of a graded commutative and associative algebra on We show that it yields a structure of Gerstenhaber and Batalin-Vilkovisky algebras.
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Keywords and phrases: string topology, topological robotics, Gerstenhaber algebra, Batalin-Vilkovisky algebra.
Received: January 15, 2022; Accepted: March 3, 2022; Published: September 24, 2022
How to cite this article: Ettaki Ayoub, My Ismail Mamouni and Mohamed Abdou Elomary, String topological robotics 2, JP Journal of Algebra, Number Theory and Applications 58 (2022), 1-18. http://dx.doi.org/10.17654/0972555522031
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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