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Loop homotopy of $6$–manifolds over $4$–manifolds

Ruizhi Huang

Algebraic & Geometric Topology 23 (2023) 2369–2388
Bibliography
1 J Amorós, I Biswas, Compact Kähler manifolds with elliptic homotopy type, Adv. Math. 224 (2010) 1167 MR2628808
2 D Barden, Simply connected five-manifolds, Ann. of Math. (2) 82 (1965) 365 MR184241
3 S Basu, The homotopy type of the loops on (n1)–connected (2n+1)–manifolds, from: "Algebraic topology and related topics" (editors M Singh, Y Song, J Wu), Springer (2019) 1 MR3991174
4 S Basu, S Basu, Homotopy groups of highly connected manifolds, Adv. Math. 337 (2018) 363 MR3853054
5 H J Baues, The degree of maps between certain 6–manifolds, Compositio Math. 110 (1998) 51 MR1601662
6 P Beben, S Theriault, The loop space homotopy type of simply-connected four-manifolds and their generalizations, Adv. Math. 262 (2014) 213 MR3228428
7 P Beben, S Theriault, Homotopy groups of highly connected Poincaré duality complexes, Doc. Math. 27 (2022) 183 MR4398609
8 P Beben, J Wu, The homotopy type of a Poincaré duality complex after looping, Proc. Edinb. Math. Soc. 58 (2015) 581 MR3391363
9 A Berglund, Koszul spaces, Trans. Amer. Math. Soc. 366 (2014) 4551 MR3217692
10 G Boyde, p–hyperbolicity of homotopy groups via K–theory, Math. Z. 301 (2022) 977 MR4405674
11 F R Cohen, Applications of loop spaces to some problems in topology, from: "Advances in homotopy theory" (editors S M Salamon, B Steer, W A Sutherland), London Math. Soc. Lecture Note Ser. 139, Cambridge Univ. Press (1989) 11 MR1055864
12 F R Cohen, J C Moore, J A Neisendorfer, The double suspension and exponents of the homotopy groups of spheres, Ann. of Math. (2) 110 (1979) 549 MR554384
13 F R Cohen, J C Moore, J A Neisendorfer, Torsion in homotopy groups, Ann. of Math. (2) 109 (1979) 121 MR519355
14 D Crowley, C M Escher, A classification of S3–bundles over S4, Differential Geom. Appl. 18 (2003) 363 MR1975035
15 D Crowley, J Nordström, The classification of 2–connected 7–manifolds, Proc. Lond. Math. Soc. 119 (2019) 1 MR3957830
16 H Duan, C Liang, Circle bundles over 4–manifolds, Arch. Math. (Basel) 85 (2005) 278 MR2172386
17 Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
18 F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, 20, Vieweg (1992) MR1189136
19 R Huang, Suspension homotopy of 6–manifolds, Algebr. Geom. Topol. 23 (2023) 439 MR4568008
20 R Huang, S Theriault, Loop space decompositions of (2n2)–connected (4n1)–dimensional Poincaré duality complexes, Res. Math. Sci. 9 (2022) 53 MR4462879
21 I M James, On the suspension sequence, Ann. of Math. (2) 65 (1957) 74 MR83124
22 Y Jiang, Regular circle actions on 2–connected 7–manifolds, J. Lond. Math. Soc. 90 (2014) 373 MR3263956
23 P E Jupp, Classification of certain 6–manifolds, Proc. Cambridge Philos. Soc. 73 (1973) 293 MR314074
24 M Kreck, On the classification of 1–connected 7–manifolds with torsion free second homology, J. Topol. 11 (2018) 720 MR3830881
25 M Kreck, Y Su, On 5–manifolds with free fundamental group and simple boundary links in S5, Geom. Topol. 21 (2017) 2989 MR3687112
26 J Neisendorfer, Algebraic methods in unstable homotopy theory, 12, Cambridge Univ. Press (2010) MR2604913
27 J Neisendorfer, T Miller, Formal and coformal spaces, Illinois J. Math. 22 (1978) 565 MR500938
28 J A Neisendorfer, P S Selick, Some examples of spaces with or without exponents, from: "Current trends in algebraic topology, I" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 343 MR686124
29 S Oka, review of Yam (1982)
30 S Sasao, On homotopy type of certain complexes, Topology 3 (1965) 97 MR171281
31 T So, S Theriault, The suspension of a 4–manifold and its applications, preprint (2019) arXiv:1909.11129
32 H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR0143217
33 C T C Wall, Classification of (n1)–connected 2n–manifolds, Ann. of Math. (2) 75 (1962) 163 MR145540
34 C T C Wall, Classification problems in differential topology, V : On certain 6–manifolds, Invent. Math. 1 (1966) 355 MR215313
35 C T C Wall, Classification problems in differential topology, VI : Classification of (s1)–connected (2s+1)–manifolds, Topology 6 (1967) 273 MR216510
36 K Yamaguchi, On the homotopy type of CW complexes with the form S2 e4 e6, Kodai Math. J. 5 (1982) 303 MR672527
37 A V Zhubr, Classification of simply connected six-dimensional spinor manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975) 839 MR0385879
38 A V Zhubr, Closed simply connected six-dimensional manifolds: proofs of classification theorems, Algebra i Analiz 12 (2000) 126 MR1793619