Algebraic & Geometric Topology Volume 13, issue 2 (2013)

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Topological complexity of motion planning in projective product spaces

Jesús González, Mark Grant, Enrique Torres-Giese and Miguel Xicoténcatl

Algebraic & Geometric Topology 13 (2013) 1027–1047

DOI: 10.2140/agt.2013.13.1027

Bibliography

1	J F Adams, Geometric dimension of bundles over $\mathrm{RP}^{n}$, from: "Proceedings of the International Conference on Prospects in Mathematics", Res. Inst. Math. Sci., Kyoto Univ., Kyoto (1974) 1 MR0482761
2	J Adem, S Gitler, I M James, On axial maps of a certain type, Bol. Soc. Mat. Mexicana 17 (1972) 59 MR0336757
3	L Astey, D M Davis, J González, Generalized axial maps and Euclidean immersions of lens spaces, Bol. Soc. Mat. Mexicana 9 (2003) 151 MR1988595
4	I Berstein, On the Lusternik–Schnirelmann category of Grassmannians, Math. Proc. Cambridge Philos. Soc. 79 (1976) 129 MR0400212
5	H Colman, M Grant, Equivariant topological complexity, Algebr. Geom. Topol. 12 (2012) 2299
6	A Costa, M Farber, Motion planning in spaces with small fundamental groups, Commun. Contemp. Math. 12 (2010) 107 MR2649230
7	D M Davis, Projective product spaces, J. Topol. 3 (2010) 265 MR2651360
8	M Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003) 211 MR1957228
9	M Farber, Invitation to topological robotics, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich (2008) MR2455573
10	M Farber, S Tabachnikov, S Yuzvinsky, Topological robotics: motion planning in projective spaces, Int. Math. Res. Not. 2003 (2003) 1853 MR1988783
11	J García-Calcines, L Vandembroucq, Topological complexity and the homotopy cofibre of the diagonal map, to appear in Math. Z. (2012)
12	C G Gibson, K Wirthmüller, A A du Plessis, E J N Looijenga, Topological stability of smooth mappings, Lecture Notes in Mathematics 552, Springer (1976) MR0436203
13	M Golubitsky, V Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics 14, Springer (1973) MR0341518
14	J González, Topological robotics in lens spaces, Math. Proc. Cambridge Philos. Soc. 139 (2005) 469 MR2177172
15	J González, E Torres-Giese, M Velasco-Fuentes, in preparation
16	M Grant, Topological complexity, fibrations and symmetry, Topology Appl. 159 (2012) 88 MR2852952
17	V Guillemin, V Ginzburg, Y Karshon, Moment maps, cobordisms, and Hamiltonian group actions, Mathematical Surveys and Monographs 98, American Mathematical Society (2002) MR1929136
18	A Haefliger, M W Hirsch, Immersions in the stable range, Ann. of Math. 75 (1962) 231 MR0143224
19	M W Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959) 242 MR0119214
20	I M James, On the immersion problem for real projective spaces, Bull. Amer. Math. Soc. 69 (1963) 231 MR0144355
21	K Y Lam, Construction of nonsingular bilinear maps, Topology 6 (1967) 423 MR0217805
22	K Y Lam, Sectioning vector bundles over real projective spaces, Quart. J. Math. Oxford Ser. 23 (1972) 97 MR0296965
23	K Y Lam, D Randall, Geometric dimension of bundles on real projective spaces, from: "Homotopy theory and its applications" (editors A Adem, R J Milgram, D C Ravenel), Contemp. Math. 188, Amer. Math. Soc. (1995) 137 MR1349135
24	G Lupton, J Scherer, Topological complexity of $H$–spaces, Proc. Amer. Math. Soc. 141 (2013) 1827 MR3020869
25	S Melikhov, Singular fibers of generic smooth maps of negative codimension
26	R J Milgram, Immersing projective spaces, Ann. of Math. 85 (1967) 473 MR0211412
27	J Oprea, J Walsh, Quotient maps, group actions and Lusternik–Schnirelmann category, Topology Appl. 117 (2002) 285 MR1874091
28	B J Sanderson, A non-immersion theorem for real projective space, Topology 2 (1963) 209 MR0151987
29	A Verona, Stratified mappings—structure and triangulability, Lecture Notes in Mathematics 1102, Springer (1984) MR771120