Algebraic & Geometric Topology Volume 19, issue 4 (2019)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Bredon cohomology and robot motion planning

Michael Farber, Mark Grant, Gregory Lupton and John Oprea

Algebraic & Geometric Topology 19 (2019) 2023–2059

DOI: 10.2140/agt.2019.19.2023

Bibliography

1	A Boudjaj, Y Rami, On spaces of topological complexity two, preprint (2016) arXiv:1607.05346v2
2	G E Bredon, Equivariant cohomology theories, 34, Springer (1967) MR0214062
3	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
4	D C Cohen, G Pruidze, Motion planning in tori, Bull. Lond. Math. Soc. 40 (2008) 249 MR2414784
5	D C Cohen, L Vandembroucq, Topological complexity of the Klein bottle, J. Appl. Comput. Topol. 1 (2017) 199
6	O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, 103, Amer. Math. Soc. (2003) MR1990857
7	A Costa, M Farber, Motion planning in spaces with small fundamental groups, Commun. Contemp. Math. 12 (2010) 107 MR2649230
8	T tom Dieck, Transformation groups, 8, de Gruyter (1987) MR889050
9	A Dranishnikov, The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfaces, Proc. Amer. Math. Soc. 144 (2016) 4999 MR3544546
10	A N Dranishnikov, Y B Rudyak, On the Berstein–Svarc theorem in dimension 2, Math. Proc. Cambridge Philos. Soc. 146 (2009) 407 MR2475974
11	S Eilenberg, T Ganea, On the Lusternik–Schnirelmann category of abstract groups, Ann. of Math. 65 (1957) 517 MR0085510
12	M Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003) 211 MR1957228
13	M Farber, Topology of robot motion planning, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 185 MR2276952
14	M Farber, Invitation to topological robotics, Eur. Math. Soc. (2008) MR2455573
15	M Farber, Configuration spaces and robot motion planning algorithms, from: "Combinatorial and toric homotopy" (editors A Darby, J Grbic, Z Lü, J Wu), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 35, World Sci. (2018) 263 MR3792464
16	M Farber, M Grant, G Lupton, J Oprea, An upper bound for topological complexity, Topology Appl. 255 (2019) 109 MR3905237
17	M Farber, S Mescher, On the topological complexity of aspherical spaces, preprint (2017) arXiv:1708.06732
18	M Farber, J Oprea, Higher topological complexity of aspherical spaces, Topology Appl. 258 (2019) 142 MR3924508
19	M Farber, S Tabachnikov, S Yuzvinsky, Topological robotics: motion planning in projective spaces, Int. Math. Res. Not. 2003 (2003) 1853 MR1988783
20	M Farber, S Yuzvinsky, Topological robotics: subspace arrangements and collision free motion planning, from: "Geometry, topology, and mathematical physics" (editors V M Buchstaber, I M Krichever), Amer. Math. Soc. Transl. Ser. 2 212, Amer. Math. Soc. (2004) 145 MR2070052
21	M Fluch, On Bredon (co-)homological dimensions of groups, PhD thesis, University of Southhampton (2011) arXiv:1009.4633
22	M Grant, Topological complexity, fibrations and symmetry, Topology Appl. 159 (2012) 88 MR2852952
23	M Grant, G Lupton, J Oprea, Spaces of topological complexity one, Homology Homotopy Appl. 15 (2013) 73 MR3117387
24	M Grant, G Lupton, J Oprea, A mapping theorem for topological complexity, Algebr. Geom. Topol. 15 (2015) 1643 MR3361146
25	M Grant, G Lupton, J Oprea, New lower bounds for the topological complexity of aspherical spaces, Topology Appl. 189 (2015) 78 MR3342573
26	M Grant, D Recio-Mitter, Topological complexity of subgroups of Artin’s braid groups, from: "Topological complexity and related topics" (editors M Grant, G Lupton, L Vandembroucq), Contemp. Math. 702, Amer. Math. Soc. (2018) 165 MR3762839
27	D Husemoller, Fibre bundles, McGraw-Hill (1966) MR0229247
28	W Lück, Transformation groups and algebraic K–theory, 1408, Springer (1989) MR1027600
29	W Lück, Survey on classifying spaces for families of subgroups, from: "Infinite groups: geometric, combinatorial and dynamical aspects" (editors L Bartholdi, T Ceccherini-Silberstein, T Smirnova-Nagnibeda, A Zuk), Progr. Math. 248, Birkhäuser (2005) 269 MR2195456
30	S Mac Lane, Homology, 114, Academic (1963) MR0156879
31	J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
32	J Milnor, On spaces having the homotopy type of a CW–complex, Trans. Amer. Math. Soc. 90 (1959) 272 MR0100267
33	G Mislin, Equivariant K–homology of the classifying space for proper actions, from: "Proper group actions and the Baum–Connes conjecture", Birkhäuser (2003) 1 MR2027169
34	Y Rudyak, On topological complexity of Eilenberg–MacLane spaces, Topology Proc. 48 (2016) 65 MR3340274
35	A S Schwarz, The genus of a fiber space, Trudy Moskov. Mat. Obšč. 10 (1961) 217 MR0154284
36	A S Schwarz, The genus of a fiber space, Trudy Moskov Mat. Obšč. 11 (1962) 99 MR0151982
37	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508