Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Manifolds with small topological complexity

Petar Pavešić

Algebraic & Geometric Topology 24 (2024) 1713–1723
Bibliography
1 D Barden, Simply connected five-manifolds, Ann. of Math. 82 (1965) 365 MR0184241
2 I Bokor, D Crowley, S Friedl, F Hebestreit, D Kasproswki, M Land, J Nicholson, Connected sum decompositions of high-dimensional manifolds, from: "2019–20 MATRIX annals" (editors D R Wood, J de Gier, C E Praeger, T Tao), MATRIX Book Ser. 4, Springer (2021) 5 MR4294760
3 D C Cohen, Topological complexity of classical configuration spaces and related objects, from: "Topological complexity and related topics" (editors M Grant, G Lupton, L Vandembroucq), Contemp. Math. 702, Amer. Math. Soc. (2018) 41 MR3762831
4 D C Cohen, L Vandembroucq, Topological complexity of the Klein bottle, J. Appl. Comput. Topol. 1 (2017) 199 MR3975552
5 O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, 103, Amer. Math. Soc. (2003) MR1990857
6 A Dranishnikov, On topological complexity of non-orientable surfaces, Topology Appl. 232 (2017) 61 MR3720882
7 A N Dranishnikov, M G Katz, Y B Rudyak, Small values of the Lusternik–Schnirelmann category for manifolds, Geom. Topol. 12 (2008) 1711 MR2421138
8 M Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003) 211 MR1957228
9 J González, M Grant, L Vandembroucq, Hopf invariants for sectional category with applications to topological robotics, Q. J. Math. 70 (2019) 1209 MR4045098
10 M Grant, G Lupton, J Oprea, Spaces of topological complexity one, Homology Homotopy Appl. 15 (2013) 73 MR3117387
11 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
12 P Hilton, G Mislin, J Roitberg, Localization of nilpotent groups and spaces, 15, North-Holland (1975) MR0478146
13 P Hilton, J Roitberg, On principal S3–bundles over spheres, Ann. of Math. 90 (1969) 91 MR0246320
14 P J Hilton, J Roitberg, On the classification problem for H–spaces of rank two, Comment. Math. Helv. 45 (1970) 506 MR0296937
15 I M James, J H C Whitehead, The homotopy theory of sphere bundles over spheres, I, Proc. Lond. Math. Soc. 4 (1954) 196 MR0061838
16 M Kapovich, J J Millson, Universality theorems for configuration spaces of planar linkages, Topology 41 (2002) 1051 MR1923214
17 M Kreck, W Lück, Topological rigidity for non-aspherical manifolds, Pure Appl. Math. Q. 5 (2009) 873 MR2532709
18 S Mescher, Spherical complexities with applications to closed geodesics, Algebr. Geom. Topol. 21 (2021) 1021 MR4250520
19 J O’Hara, The configuration space of planar spidery linkages, Topology Appl. 154 (2007) 502 MR2278700
20 P Pavešić, A topologist’s view of kinematic maps and manipulation complexity, from: "Topological complexity and related topics" (editors M Grant, G Lupton, L Vandembroucq), Contemp. Math. 702, Amer. Math. Soc. (2018) 61 MR3762832
21 P Pavešić, Topological complexity of a map, Homology Homotopy Appl. 21 (2019) 107 MR3921612
22 P Pavešić, Monotonicity of the Schwarz genus, Proc. Amer. Math. Soc. 148 (2020) 1339 MR4055959
23 P A Schweitzer, Secondary cohomology operations induced by the diagonal mapping, Topology 3 (1965) 337 MR0182969
24 N Shvalb, M Shoham, D Blanc, The configuration space of arachnoid mechanisms, Forum Math. 17 (2005) 1033 MR2195717
25 W Singhof, On the Lusternik–Schnirelmann category of Lie groups, Math. Z. 145 (1975) 111 MR0391075
26 S Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. 74 (1961) 391 MR0137124
27 C T C Wall, Classification of (n1)–connected 2n–manifolds, Ann. of Math. 75 (1962) 163 MR0145540