Algebraic & Geometric Topology Volume 14, issue 4 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Higher topological complexity and its symmetrization

Ibai Basabe, Jesús González, Yuli B Rudyak and Dai Tamaki

Algebraic & Geometric Topology 14 (2014) 2103–2124

DOI: 10.2140/agt.2014.14.2103

Bibliography

1	I Basabe, J González, Y Rudyak, D Tamaki, Higher topological complexity and its symmetrization, arXiv:1009.1851
2	G E Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics 46, Academic Press (1972) MR0413144
3	O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, Math. Surveys Monographs 103, Amer. Math. Soc. (2003) MR1990857
4	A Dold, Lectures on algebraic topology, Classics in Mathematics, Springer, Berlin (1995) MR1335915
5	M Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003) 211 MR1957228
6	M Farber, Instabilities of robot motion, Topology Appl. 140 (2004) 245 MR2074919
7	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, Dordrecht (2006) 185 MR2276952
8	M Farber, Invitation to topological robotics, Zurich Lectures Adv. Math. 10, Eur. Math. Soc. (2008) MR2455573
9	M Farber, M Grant, Symmetric motion planning, from: "Topology and robotics" (editors M Farber, R Ghrist, M Burger, D Koditschek), Contemp. Math. 438, Amer. Math. Soc. (2007) 85 MR2359031
10	M Farber, M Grant, Robot motion planning, weights of cohomology classes, and cohomology operations, Proc. Amer. Math. Soc. 136 (2008) 3339 MR2407101
11	M Farber, S Tabachnikov, S Yuzvinsky, Topological robotics: Motion planning in projective spaces, Int. Math. Res. Not. 2003 (2003) 1853 MR1988783
12	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
13	E M Feichtner, G M Ziegler, The integral cohomology algebras of ordered configuration spaces of spheres, Doc. Math. 5 (2000) 115 MR1752611
14	A M Gleason, Spaces with a compact Lie group of transformations, Proc. Amer. Math. Soc. 1 (1950) 35 MR0033830
15	J González, P Landweber, Symmetric topological complexity of projective and lens spaces, Algebr. Geom. Topol. 9 (2009) 473 MR2491582
16	N Iwase, M Sakai, Topological complexity is a fibrewise L–S category, Topology Appl. 157 (2010) 10 MR2556074
17	J W Jaworowski, Extensions of $G$–maps and Euclidean $G$–retracts, Math. Z. 146 (1976) 143 MR0394550
18	S Kallel, Symmetric products, duality and homological dimension of configuration spaces, from: "Groups, homotopy and configuration spaces" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13 (2008) 499 MR2508221
19	R Karasev, P Landweber, Estimating the higher symmetric topological complexity of spheres, Algebr. Geom. Topol. 12 (2012) 75 MR2889546
20	J C Latombe, Robot motion planning, Kluwer Int. Series Engin. Comp. Sci. 124, Kluwer Academic (1991)
21	S M LaValle, Planning algorithms, Cambridge Univ. Press (2006) MR2424564
22	G Lupton, J Scherer, Topological complexity of $H$–spaces, Proc. Amer. Math. Soc. 141 (2013) 1827 MR3020869
23	Y B Rudyak, On higher analogs of topological complexity, Topology Appl. 157 (2010) 916 MR2593704
24	A S Švarc, The genus of a fiber space, Dokl. Akad. Nauk SSSR 119 (1958) 219 MR0102812