Derfoufi, Y. and Mamouni, M.I. (2016) String topological robotics. JP Journal of Geometry and Topology, 19 (3). pp. 189-208.

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Abstract

We claim here to link two well known theories; namely the string topology (founded by Chas and Sullivan in 3) and the topological robotics (founded by Farber some few years later, in 7). For our purpose, we consider G a compact Lie group acting transitively on a path connected n-manifold X. On the set MLP(X) of the so-called loop motion planning algorithms, we define and discuss the notion of transversality. Firstly, we define an intersection loop motion planning product at level of chains of MLP(X). Secondly, we define aboundary operator on the chains of MLP(X) and extend this intersection product at level of homology to a string loop motion planning product. Finally, we show that this string product induces on the shifted string loop motion planning homology ℍ∗(MLP(X)):= H∗+2n M(LP(X)) a structure of an associative and commutative graded algebra (acga). By the end, we ask how one may extend this acga-structure to a structure of Gerstenhaber algebra or that of a Batalin-Vilkovisky algebra. Some ideas will be suggested. © 2016 Pushpa Publishing House, Allahabad, India.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/3985

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