Volume 23, issue 6 (2019)

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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