The geometry and topology of reconfiguration

Advances in Applied Mathematics

Volumn 38, Issue 3, 2007, Pages 302-323

  Ghrist, R ^a   Peterson, V ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

CAT(0) geometry; Configuration space; Nonpositive curvature

Indexed keywords

COMBINATORIAL MATHEMATICS; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING; TOPOLOGY;

CAT(0) GEOMETRY; CONFIGURATION SPACE; NONPOSITIVE CURVATURE;

STATE ESTIMATION;

EID: 33846842337     PISSN: 01968858     EISSN: 10902074     Source Type: Journal    
DOI: 10.1016/j.aam.2005.08.009     Document Type: Article

References (34)

1. A. Abrams, Configuration spaces and braid groups of graphs, PhD thesis, UC Berkeley, 2000
2. Abrams A., and Ghrist R. Finding topology in a factory: Configuration spaces. Amer. Math. Monthly 109 (2002) 140-150
3. Abrams A., and Ghrist R. State complexes for metamorphic robot systems. Internat. J. Robotics Research 23 (2004) 809-824
4. S. Alexander, R. Bishop, R. Ghrist, Pursuit and evasion on non-convex domains of arbitrary dimensions, in: Proc. Robotics: Systems and Science, 2006
5. Billera L., Holmes S., and Vogtmann K. Geometry of the space of phylogenetic trees. Adv. in Appl. Math. 27 (2001) 733-767
6. Bridson M., and Haefliger A. Metric Spaces of Nonpositive Curvature (1999), Springer-Verlag, Berlin
7. Charney R. The Tits conjecture for locally reducible Artin groups. Internat. J. Algebra Comput. 10 (2000) 783-797
8. G. Chirikjian, Kinematics of a metamorphic robotic system, in: Proc. IEEE ICRA, 1994
9. Crisp J., and Wiest B. Embeddings of graph braid groups and surface groups in right-angled Artin groups and braids groups. Algebr. Geom. Topol. 4 (2004) 439-472
10. P. Csorba, F. Lutz, Graph coloring manifolds, Preprint, 2005, Contemp. Math., in press
11. Davis M. Groups generated by reflections and aspherical manifolds not covered by Euclidean space. Ann. of Math. 117 2 (1983) 293-324
12. Davis M., and Januszkiewicz T. Right angled Artin groups are commensurable with right angled Coxeter groups. J. Pure Appl. Algebra 153 (2000) 229-235
13. Fair R.B., Srinivasan V., Ren H., Paik P., Pamula V.K., and Pollack M.G. Electrowetting based on chip sample processing for integrated microfluidics. IEEE Inter. Electron Devices Meeting (IEDM) (2003)
14. R.B. Fair, A. Khlystov, V. Srinivasan, V.K. Pamula, K.N. Weaver, Integrated chemical/biochemical sample collection, pre-concentration, and analysis on a digital microfluidic lab-on-a-chip platform, in: Lab-on-a-Chip: Platforms, Devices, and Applications, Conf. 5591, SPIE Optics East, Philadelphia, Oct. 25-28, 2004
15. Farley D. Finiteness and CAT(0) properties of diagram groups. Topology 42 (2003) 1065-1082
16. Gaucher P. About the globular homology of higher dimensional automata. Cahiers de Top. et Geom. Diff. Categoriques 43 2 (2002) 107-156
17. R. Ghrist, Shape complexes for metamorphic robot systems, in: Algorithmic Foundations of Robotics V, STAR 7 (2004) 185-201
18. Ghrist R. Configuration spaces braid groups on graphs in robotics. AMS/IP Stud. Math. 24 (2001) 29-40
19. Ghrist R., and Koditschek D. Safe, cooperative robot dynamics on graphs. SIAM J. Control Optim. 40 (2002) 1556-1575
20. R. Ghrist, S. LaValle, Nonpositive curvature and Pareto optimal motion planning, SIAM J. Control Optim., 2006, in press
21. Ghrist R., O'Kane J., and LaValle S.M. Computing Pareto optimal coordinations on roadmaps. Internat. J. Robotics Research 12 (2006) 997-1012
22. Gromov M. Hyperbolic groups. Essays in Group Theory. MSRI Publ. vol. 8 (1987), Springer-Verlag
23. E. Goubault, Schedulers as interpreters of higher-dimensional automata, in: Proc. Workshop on Partial Evaluation and Semantic-Based Program Manipulation (PEPM), 1995
24. F. Haglund, D. Wise, Special cube complexes, preprint, March 2005
25. Lovász L. Kneser's conjecture, chromatic number, and homotopy. J. Combin. Theory Ser. A 25 (1978) 319-324
26. Niblo G.A., and Reeves L.D. The geometry of cube complexes and the complexity of their fundamental groups. Topology 37 (1998) 621-633
27. V. Pratt, Modelling concurrency with geometry, in: Proc. 18th Symp. on Principles of Programming Languages, 1991
28. Raussen M. State spaces and dipaths up to dihomotopy. Homotopy, Homology, Appl. 5 (2003) 257-280
29. Raussen M. On the classification of dipaths in geometric models of concurrency. Math. Structures Comp. Sci. 10 (2000) 427-457
30. Reeves L.D. Rational subgroups of cubed 3-manifold groups. Michigan Math. J. 42 (1995) 109-126
31. Reutenauer C. The Mathematics of Petri Nets (1990), Prentice Hall
32. Sali A., Shakhnovich E., and Karplus M. How does a protien fold?. Nature 369 (1994) 248-251
33. Sali A., Shakhnovich E., and Karplus M. Kinetics of protein folding. J. Mol. Biol. 235 (1994) 1614-1636
34. Swiatkowski J. Estimates for homological dimension of configuration spaces of graphs. Colloq. Math. 89 (2001) 69-79