Algebraic & Geometric Topology Volume 23, issue 7 (2023)

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

Neighboring mapping points theorem

Andrei V Malyutin and Oleg R Musin

Algebraic & Geometric Topology 23 (2023) 3043–3070

DOI: 10.2140/agt.2023.23.3043

Bibliography

1	C Adams, F Morgan, J M Sullivan, When soap bubbles collide, Amer. Math. Monthly 114 (2007) 329 MR2281929
2	H Adams, J Bush, F Frick, Metric thickenings, Borsuk–Ulam theorems, and orbitopes, Mathematika 66 (2020) 79 MR4130314
3	A Akopyan, R Karasev, A Volovikov, Borsuk–Ulam type theorems for metric spaces, preprint (2012) arXiv:1209.1249
4	R Alexander, The width and diameter of a simplex, Geometriae Dedicata 6 (1977) 87 MR470859
5	I Bárány, P V M Blagojević, G M Ziegler, Tverberg’s theorem at 50 : extensions and counterexamples, Not. Amer. Math. Soc. 63 (2016) 732 MR3495518
6	I Bárány, P Soberón, Tverberg’s theorem is 50 years old : a survey, Bull. Amer. Math. Soc. 55 (2018) 459 MR3854075
7	S A Bogatyĭ, The topological Helly theorem, Fundam. Prikl. Mat. 8 (2002) 365 MR1939252
8	L Danzer, B Grünbaum, V Klee, Helly’s theorem and its relatives, from: "Convexity", Proc. Sympos. Pure Math. 7, Amer. Math. Soc. (1963) 101 MR0157289
9	B V Dekster, The Jung theorem for spherical and hyperbolic spaces, Acta Math. Hungar. 67 (1995) 315 MR1315815
10	E Denne, J M Sullivan, The distortion of a knotted curve, Proc. Amer. Math. Soc. 137 (2009) 1139 MR2457456
11	F Frick, Counterexamples to the topological Tverberg conjecture, from: "Geometric and algebraic combinatorics" (editors G Kalai, I Novik, F Santos, V Welker), Oberwolfach Rep. 12 (2015) 318 MR3443113
12	M Gromov, Homotopical effects of dilatation, J. Differential Geometry 13 (1978) 303 MR551562
13	M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
14	B Grünbaum, On the facial structure of convex polytopes, Bull. Amer. Math. Soc. 71 (1965) 559 MR182966
15	W Gustin, Review of Verfitw (1952)
16	N V Ivanov, Leray theorems in bounded cohomology theory, preprint (2020) arXiv:2012.08038
17	R N Karasëv, Topological methods in combinatorial geometry, Uspekhi Mat. Nauk 63 (2008) 39 MR2492772
18	R N Karasev, A topological central point theorem, Topology Appl. 159 (2012) 864 MR2868886
19	V Klee, Review of Tim65 (1965)
20	A V Malyutin, On the question of genericity of hyperbolic knots, Int. Math. Res. Not. 2020 (2020) 7792 MR4176838
21	A V Malyutin, O R Musin, Borsuk–Ulam type theorems for Delaunay maps, in preparation
22	J Matoušek, Using the Borsuk–Ulam theorem, Springer (2003) MR1988723
23	B Matschke, A survey on the square peg problem, Not. Amer. Math. Soc. 61 (2014) 346 MR3184501
24	L Montejano, A new topological Helly theorem and some transversal results, Discrete Comput. Geom. 52 (2014) 390 MR3249387
25	K Morita, On the dimension of normal spaces, II, J. Math. Soc. Japan 2 (1950) 16 MR39990
26	K Morita, On generalizations of Borsuk’s homotopy extension theorem, Fund. Math. 88 (1975) 1 MR375220
27	O R Musin, Homotopy invariants of covers and KKM-type lemmas, Algebr. Geom. Topol. 16 (2016) 1799 MR3523055
28	O R Musin, KKM type theorems with boundary conditions, J. Fixed Point Theory Appl. 19 (2017) 2037 MR3692438
29	O R Musin, J Wu, Cobordism classes of maps and covers for spheres, Topology Appl. 237 (2018) 21 MR3760773
30	N Noble, Poorly separated infinite normal products, preprint (2020) arXiv:2002.02483
31	J Pardon, On the distortion of knots on embedded surfaces, Ann. of Math. 174 (2011) 637 MR2811613
32	E Schechter, Handbook of analysis and its foundations, Academic (1997) MR1417259
33	A B Skopenkov, Topological Tverberg conjecture, Uspekhi Mat. Nauk 73 (2018) 141 MR3780070
34	M Starbird, The Borsuk homotopy extension theorem without the binormality condition, Fund. Math. 87 (1975) 207 MR372810
35	H Steinlein, Borsuk’s antipodal theorem and its generalizations and applications : a survey, from: "Topological methods in nonlinear analysis" (editor A Granas), Sém. Math. Sup. 95, Presses Univ. Montréal (1985) 166 MR801938
36	H Steinlein, Spheres and symmetry : Borsuk’s antipodal theorem, Topol. Methods Nonlinear Anal. 1 (1993) 15 MR1215255
37	V M Tikhomirov, Some questions of the approximation theory, Izdat. Moskov. Univ. (1976) 304 MR0487161
38	T A Timan, Proof of a geometric theorem of Jung, and its analogue in the theory of stochastic processes, Uspehi Mat. Nauk 20 (1965) 213 MR0183000
39	S Verblunsky, On the circumradius of a bounded set, J. London Math. Soc. 27 (1952) 505 MR51539