Algebraic & Geometric Topology Volume 11, issue 2 (2011)

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

Configuration-like spaces and coincidences of maps on orbits

R N Karasev and A Yu Volovikov

Algebraic & Geometric Topology 11 (2011) 1033–1052

DOI: 10.2140/agt.2011.11.1033

Bibliography

1	T Bartsch, On the genus of representation spheres, Comment. Math. Helv. 65 (1990) 85 MR1036130
2	T Bartsch, Topological methods for variational problems with symmetries, 1560, Springer (1993) MR1295238
3	I Basabe, J Gonzalez, Y B Rudyak, D Tamaki, Higher topological complexity and homotopy dimension of configuration spaces on spheres arXiv:1009.1851
4	D V Bolotov, The Cohen–Lusk conjecture, Mat. Zametki 70 (2001) 22 MR1883046
5	K Borsuk, Drei Sätze über die n–dimensionale euklidische Sphäre, Fund. Math. 20 (1933) 177
6	M Clapp, D Puppe, Invariants of the Lusternik–Schnirelmann type and the topology of critical sets, Trans. Amer. Math. Soc. 298 (1986) 603 MR860382
7	M Clapp, D Puppe, Critical point theory with symmetries, J. Reine Angew. Math. 418 (1991) 1 MR1111200
8	F Cohen, E L Lusk, Configuration-like spaces and the Borsuk–Ulam theorem, Proc. Amer. Math. Soc. 56 (1976) 313 MR0425949
9	P E Conner, E E Floyd, On the construction of periodic maps without fixed points, Proc. Amer. Math. Soc. 10 (1959) 354 MR0105115
10	P E Conner, E E Floyd, Fixed point free involutions and equivariant maps, Bull. Amer. Math. Soc. 66 (1960) 416 MR0163310
11	R N Karasev, The genus and the category of configuration spaces, Topology Appl. 156 (2009) 2406 MR2547785
12	R N Karasev, Periodic billiard trajectories in smooth convex bodies, Geom. Funct. Anal. 19 (2009) 423 MR2545244
13	R N Karasev, A Y Volovikov, Knaster’s problem for almost (Z_p)^k–orbits, Topology Appl. 157 (2010) 941 MR2593707
14	B Knaster, Problem 4, Colloq. Math. 30 (1947) 30
15	M A Krasnosel’skiĭ, On the estimation of the number of critical points of functionals, Uspehi Matem. Nauk (N.S.) 7 (1952) 157 MR0048699
16	M A Krasnosel’skiĭ, On special coverings of a finite-dimensional sphere, Dokl. Akad. Nauk SSSR (N.S.) 103 (1955) 961 MR0081454
17	M A Krasnosel’skiĭ, Stability of the critical values of even functionals on the sphere, Mat. Sb. N.S. 37(79) (1955) 301 MR0079740
18	V V Makeev, The Knaster problem and almost spherical sections, Mat. Sb. 180 (1989) 424 MR993234
19	F Roth, On the category of Euclidean configuration spaces and associated fibrations, from: "Groups, homotopy and configuration spaces", Geom. Topol. Monogr. 13 (2008) 447 MR2508218
20	A S Schwarz, Some estimates of the genus of a topological space in the sense of Krasnosel’skiĭ, Uspehi Mat. Nauk (N.S.) 12 (1957) 209 MR0090055
21	A S Schwarz, The genus of a fibre space, Trudy Moskov Mat. Obšč. 11 (1962) 99 MR0151982
22	S Smale, On the topology of algorithms I, J. Complexity 3 (1987) 81 MR907191
23	V A Vasil’ev, Cohomology of braid groups and the complexity of algorithms, Funktsional. Anal. i Prilozhen. 22 (1988) 15, 96 MR961758
24	A Y Volovikov, A Bourgin–Yang-type theorem for Z_pⁿ–action, Mat. Sb. 183 (1992) 115 MR1186977
25	A Y Volovikov, On the index of G–spaces, Mat. Sb. 191 (2000) 3 MR1805595
26	A Y Volovikov, Coincidence points of mappings of Z_pⁿ–spaces, Izv. Ross. Akad. Nauk Ser. Mat. 69 (2005) 53 MR2179415
27	A Y Volovikov, On the Cohen–Lusk theorem, Fundam. Prikl. Mat. 13 (2007) 61 MR2475581
28	C T Yang, Continuous functions from spheres to euclidean spaces, Ann of Math. (2) 62 (1955) 284 MR0072471
29	C T Yang, On theorems of Borsuk–Ulam, Kakutani–Yamabe–Yujobô and Dyson II, Ann. of Math. (2) 62 (1955) 271 MR0072470