Algebraic & Geometric Topology Volume 24, issue 3 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Sequential parametrized topological complexity and related invariants

Michael Farber and John Oprea

Algebraic & Geometric Topology 24 (2024) 1755–1780

DOI: 10.2140/agt.2024.24.1755

Bibliography

1	M Bayeh, S Sarkar, Higher equivariant and invariant topological complexities, J. Homotopy Relat. Struct. 15 (2020) 397 MR4182878
2	G E Bredon, Introduction to compact transformation groups, 46, Academic (1972) MR0413144
3	D C Cohen, M Farber, S Weinberger, Topology of parametrized motion planning algorithms, SIAM J. Appl. Algebra Geom. 5 (2021) 229 MR4272901
4	D C Cohen, M Farber, S Weinberger, Parametrized topological complexity of collision-free motion planning in the plane, Ann. Math. Artif. Intell. 90 (2022) 999 MR4510496
5	H Colman, M Grant, Equivariant topological complexity, Algebr. Geom. Topol. 12 (2012) 2299 MR3020208
6	A N Dranishnikov, On the Lusternik–Schnirelmann category of spaces with 2–dimensional fundamental group, Proc. Amer. Math. Soc. 137 (2009) 1489 MR2465675
7	A Dranishnikov, The Lusternik–Schnirelmann category and the fundamental group, Algebr. Geom. Topol. 10 (2010) 917 MR2629770
8	A Dranishnikov, On topological complexity of twisted products, Topology Appl. 179 (2015) 74 MR3270927
9	M Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003) 211 MR1957228
10	M Farber, A K Paul, Sequential parametrized motion planning and its complexity, Topology Appl. 321 (2022) 108256 MR4491760
11	M Farber, S Weinberger, Parametrized motion planning and topological complexity, from: "Algorithmic foundations of robotics, XV" (editors S M LaValle, J M O’Kane, M Otte, D Sadigh, P Tokekar), Springer Proc. Adv. Robot. 25, Springer (2023) 1 MR4572863
12	M Farber, S Weinberger, Parametrized topological complexity of sphere bundles, Topol. Methods Nonlinear Anal. 61 (2023) 161 MR4583972
13	M Farber, M Grant, G Lupton, J Oprea, An upper bound for topological complexity, Topology Appl. 255 (2019) 109 MR3905237
14	R Fritsch, R A Piccinini, Cellular structures in topology, 19, Cambridge Univ. Press (1990) MR1074175
15	I M James, On category, in the sense of Lusternik–Schnirelmann, Topology 17 (1978) 331 MR0516214
16	S M LaValle, Planning algorithms, Cambridge Univ. Press (2006) MR2424564
17	J P May, A concise course in algebraic topology, Univ. Chicago Press (1999) MR1702278
18	J Oprea, J Strom, Mixing categories, Proc. Amer. Math. Soc. 139 (2011) 3383 MR2811292
19	P A Ostrand, Dimension of metric spaces and Hilbert’s problem 13, Bull. Amer. Math. Soc. 71 (1965) 619 MR0177391
20	R S Palais, The classification of G–spaces, 36, Amer. Math. Soc. (1960) MR0177401
21	A K Paul, D Sen, An upper bound for higher topological complexity and higher strongly equivariant complexity, Topology Appl. 277 (2020) 107172 MR4083172
22	Y B Rudyak, On higher analogs of topological complexity, Topology Appl. 157 (2010) 916 MR2593704
23	A S Schwartz, The genus of a fibre space, Tr. Mosk. Mat. Obs. 11 (1962) 99 MR151982