Volume 9, issue 1 (2009)

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Topology of configuration space of two particles on a graph, I

Kathryn Barnett and Michael Farber

Algebraic & Geometric Topology 9 (2009) 593–624
Bibliography
1 A Abrams, Configuration spaces and braid groups of graphs, PhD thesis, UC Berkeley (2000)
2 V I Arnol′d, The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227 MR0242196
3 F R Cohen, The homology of $\mathcal C_{n+1}$–spaces, $n \ge 0$, from: "The homology of iterated loop spaces", Lecture Notes in Math. 533, Springer (1976) 207 MR0436146
4 A H Copeland Jr., Homology of deleted products in dimension one, Proc. Amer. Math. Soc. 16 (1965) 1005 MR0182968
5 A H Copeland Jr., C W Patty, Homology of deleted products of one-dimensional spaces, Trans. Amer. Math. Soc. 151 (1970) 499 MR0264651
6 A Dold, Lectures on algebraic topology, Die Grund. der math. Wissen. 200, Springer (1972) MR0415602
7 E Fadell, L Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111 MR0141126
8 M Farber, Collision free motion planning on graphs, from: "Algorithmic foundations of robotics VI", Springer Tracts in Adv. Robotics 17, Springer (2005) 123
9 M Farber, Invitation to topological robotics, Zurich Lectures in Advanced Math., Eur. Math. Soc. (2008) MR2455573
10 D Farley, Homology of tree braid groups, from: "Topological and asymptotic aspects of group theory" (editors M Farber, R Ghrist, M Burger, D Koditschek), Contemp. Math. 394, Amer. Math. Soc. (2006) 101 MR2216709
11 D Farley, Presentations for the cohomology rings of tree braid groups, from: "Topology and robotics", Contemp. Math. 438, Amer. Math. Soc. (2007) 145 MR2359035
12 D Farley, Presentations for the cohomology rings of tree braid groups, from: "Topology and robotics", Contemp. Math. 438, Amer. Math. Soc. (2007) 145 MR2359035
13 D Farley, L Sabalka, Discrete Morse theory and graph braid groups, Algebr. Geom. Topol. 5 (2005) 1075 MR2171804
14 D Farley, L Sabalka, On the cohomology rings of tree braid groups, J. Pure Appl. Algebra 212 (2008) 53 MR2355034
15 Ś R Gal, Euler characteristic of the configuration space of a complex, Colloq. Math. 89 (2001) 61 MR1853415
16 R W Ghrist, Configuration spaces and braid groups on graphs in robotics, from: "Knots, braids, and mapping class groups—papers dedicated to Joan S. Birman (New York, 1998)" (editors J Gilman, W W Menasco, X S Lin), AMS/IP Stud. Adv. Math. 24, Amer. Math. Soc. (2001) 29 MR1873106
17 R W Ghrist, D E Koditschek, Safe cooperative robot dynamics on graphs, SIAM J. Control Optim. 40 (2002) 1556 MR1882808
18 C W Patty, Homotopy groups of certain deleted product spaces, Proc. Amer. Math. Soc. 12 (1961) 369 MR0126274
19 C W Patty, The fundamental group of certain deleted product spaces, Trans. Amer. Math. Soc. 105 (1962) 314 MR0143211
20 A Shapiro, Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction, Ann. of Math. $(2)$ 66 (1957) 256 MR0089410
21 B Totaro, Configuration spaces of algebraic varieties, Topology 35 (1996) 1057 MR1404924
22 V A Vassiliev, Complements of discriminants of smooth maps: topology and applications, Transl. of Math. Monogr. 98, Amer. Math. Soc. (1992) MR1168473
23 W t Wu, On the realization of complexes in Euclidean spaces. III, Sci. Sinica 8 (1959) 133 MR0098365
24 W t Wu, A theory of imbedding, immersion, and isotopy of polytopes in a euclidean space, Science Press (1965) MR0215305