LEADER 03075nam 22004335a 450 001 9910151934503321 005 20091109150325.0 010 $a3-03719-554-1 024 70$a10.4171/054 035 $a(CKB)3710000000953830 035 $a(CH-001817-3)78-091109 035 $a(PPN)178155462 035 $a(EXLCZ)993710000000953830 100 $a20091109j20080819 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInvitation to Topological Robotics$b[electronic resource] /$fMichael Farber 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008 215 $a1 online resource (143 pages) 225 0 $aZurich Lectures in Advanced Mathematics (ZLAM) 330 $aThe book discusses several selected topics of a new emerging area of research lying on the interface between topology and engineering. The first main topic of the book is topology of configuration spaces of mechanical linkages. These manifolds arise in various fields of mathematics and in other sciences, e.g. engineering, statistics, molecular biology. To compute Betti numbers of these configuration spaces we apply a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in the book is a solution of a conjecture of Kevin Walker which states that the relative sizes of bars of a linkage are determined, up to certain equivalence, by the cohomology algebra of the linkage configuration space. The book also describes a new probabilistic approach to topology of linkages which treats the bar lengths as random variables and studies mathematical expectations of Betti numbers. The second main topic of the book is topology of configuration spaces associated to polyhedra. The book gives an account of a beautiful work of S.R. Gal suggesting an explicit formula for the generating function encoding Euler characteristics of these spaces. Next we study the knot theory of a robot arm focusing on a recent important result of R. Connelly, E. Demain and G. Rote. Finally, the book investigates topological problems arising in the theory of robot motion planning algorithms and studies the homotopy invariant TC(X) measuring navigational complexity of configuration spaces. The book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering. 606 $aAnalytic topology$2bicssc 606 $aMechanical engineering$2bicssc 606 $aGlobal analysis, analysis on manifolds$2msc 606 $aManifolds and cell complexes$2msc 615 07$aAnalytic topology 615 07$aMechanical engineering 615 07$aGlobal analysis, analysis on manifolds 615 07$aManifolds and cell complexes 686 $a58-xx$a57-xx$2msc 700 $aFarber$b Michael$056743 801 0$bch0018173 906 $aBOOK 912 $a9910151934503321 996 $aInvitation to Topological Robotics$92565448 997 $aUNINA