Volume 23, issue 6 (2019)

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

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Plato's cave and differential forms

Fedor Manin

Geometry & Topology 23 (2019) 3141–3202
Bibliography
1 M Amann, Degrees of self-maps of simply connected manifolds, Int. Math. Res. Not. 2015 (2015) 8545 MR3417685
2 P Andrews, M Arkowitz, Sullivan’s minimal models and higher order Whitehead products, Canadian J. Math. 30 (1978) 961 MR506254
3 M Arkowitz, G Lupton, Rational obstruction theory and rational homotopy sets, Math. Z. 235 (2000) 525 MR1800210
4 A Berdnikov, Lipschitz null-homotopy of mappings S3 S2, preprint (2018) arXiv:1811.02606
5 D Blanc, Homotopy operations and rational homotopy type, from: "Categorical decomposition techniques in algebraic topology" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 47 MR2039759
6 R Body, M Mimura, H Shiga, D Sullivan, p–universal spaces and rational homotopy types, Comment. Math. Helv. 73 (1998) 427 MR1633367
7 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
8 E H Brown Jr., R H Szczarba, On the rational homotopy type of function spaces, Trans. Amer. Math. Soc. 349 (1997) 4931 MR1407482
9 M Čadek, M Krčál, J Matoušek, L Vokřínek, U Wagner, Extendability of continuous maps is undecidable, Discrete Comput. Geom. 51 (2014) 24 MR3148651
10 A Calder, J Siegel, On the width of homotopies, Topology 19 (1980) 209 MR579572
11 G R Chambers, D Dotterrer, F Manin, S Weinberger, Quantitative null-cobordism, J. Amer. Math. Soc. 31 (2018) 1165 MR3836564
12 G R Chambers, F Manin, S Weinberger, Quantitative nullhomotopy and rational homotopy type, Geom. Funct. Anal. 28 (2018) 563 MR3816519
13 R Douglas, Positive weight homotopy types, Illinois J. Math. 27 (1983) 597 MR720095
14 E Dror Farjoun, Homotopy and homology of diagrams of spaces, from: "Algebraic topology" (editors H R Miller, D C Ravenel), Lecture Notes in Math. 1286, Springer (1987) 93 MR922924
15 H Edelsbrunner, D R Grayson, Edgewise subdivision of a simplex, Discrete Comput. Geom. 24 (2000) 707 MR1799608
16 H Federer, W H Fleming, Normal and integral currents, Ann. of Math. 72 (1960) 458 MR123260
17 Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
18 S Ferry, S Weinberger, Quantitative algebraic topology and Lipschitz homotopy, Proc. Natl. Acad. Sci. USA 110 (2013) 19246 MR3153953
19 M Filakovsky, P Franek, U Wanger, S Zhechev, Computing simplicial representatives of homotopy group elements, from: "Proceedings of the twenty-ninth annual ACM–SIAM symposium on discrete algorithms" (editor A Czumaj), SIAM (2018) 1135 MR3775862
20 M Filakovský, L Vokřínek, Are two given maps homotopic? An algorithmic viewpoint, Found. Comput. Math. (2019)
21 S M Gersten, Isoperimetric and isodiametric functions of finite presentations, from: "Geometric group theory, I" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 79 MR1238517
22 P A Griffiths, J W Morgan, Rational homotopy theory and differential forms, 16, Birkhäuser (1981) MR641551
23 M Gromov, Homotopical effects of dilatation, J. Differential Geometry 13 (1978) 303 MR551562
24 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, 152, Birkhäuser (1999) MR1699320
25 M Gromov, Quantitative homotopy theory, from: "Prospects in mathematics" (editor H Rossi), Amer. Math. Soc. (1999) 45 MR1660471
26 L Guth, Recent progress in quantitative topology, from: "Surveys in differential geometry 2017 : celebrating the 50th anniversary of the Journal of Differential Geometry" (editors H D Cao, J Li, R M Schoen, S T Yau), Surv. Differ. Geom. 22, International (2018) 191 MR3838118
27 A Haefliger, Plongements de variétés dans le domaine stable, from: "Séminaire Bourbaki, 1962/63", Secrétariat mathématique (1962) MR0189049
28 R M Hain, Iterated integrals and homotopy periods, 291, Amer. Math. Soc. (1984) MR727818
29 D Kotschick, On products of harmonic forms, Duke Math. J. 107 (2001) 521 MR1828300
30 J T Maher, The geometry of dilatation and distortion, PhD thesis, The University of Chicago (2004) MR2717156
31 F Manin, Asymptotic invariants of homotopy groups, PhD thesis, The University of Chicago (2015) MR3407463
32 F Manin, A zoo of growth functions of mapping class sets, J. Topol. Anal. (2018)
33 F Manin, S Weinberger, Integral and rational mapping classes, preprint (2018) arXiv:1802.05784
34 M Mimura, H Toda, On p–equivalences and p–universal spaces, Comment. Math. Helv. 46 (1971) 87 MR285007
35 A Nabutovsky, Non-recursive functions, knots “with thick ropes”, and self-clenching “thick” hyperspheres, Comm. Pure Appl. Math. 48 (1995) 381 MR1324407
36 M Nakaoka, H Toda, On Jacobi identity for Whitehead products, J. Inst. Polytech. Osaka City Univ. Ser. A. 5 (1954) 1 MR0065926
37 L Scull, Rational S1–equivariant homotopy theory, Trans. Amer. Math. Soc. 354 (2002) 1 MR1859023
38 H Shiga, Rational homotopy type and self-maps, J. Math. Soc. Japan 31 (1979) 427 MR535089
39 D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 269 MR646078