Geometry & Topology Volume 28, issue 3 (2024)

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Moduli spaces of Ricci positive metrics in dimension five

McFeely Jackson Goodman

Geometry & Topology 28 (2024) 1065–1098

DOI: 10.2140/gt.2024.28.1065

Bibliography

1	M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797
2	M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405 MR0397798
3	A Bahri, P Gilkey, The eta invariant, Pin^c bordism, and equivariant Spin^c bordism for cyclic 2–groups, Pacific J. Math. 128 (1987) 1 MR0883375
4	D Barden, Simply connected five-manifolds, Ann. of Math. 82 (1965) 365 MR0184241
5	V N Berestovskiĭ, Homogeneous Riemannian manifolds of positive Ricci curvature, Mat. Zametki 58 (1995) 334 MR1368542
6	A L Besse, Einstein manifolds, 10, Springer (1987) MR0867684
7	B Botvinnik, P B Gilkey, The eta invariant and metrics of positive scalar curvature, Math. Ann. 302 (1995) 507 MR1339924
8	B Botvinnik, M G Walsh, D J Wraith, Homotopy groups of the observer moduli space of Ricci positive metrics, Geom. Topol. 23 (2019) 3003 MR4039184
9	J P Bourguignon, Une stratification de l’espace des structures riemanniennes, Compositio Math. 30 (1975) 1 MR0418147
10	B L Burdick, Ricci-positive metrics on connected sums of projective spaces, Differential Geom. Appl. 62 (2019) 212 MR3881650
11	D Corro, F Galaz-García, Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions, Proc. Amer. Math. Soc. 148 (2020) 3087 MR4099795
12	D Crowley, C M Escher, A classification of S³–bundles over S⁴, Differential Geom. Appl. 18 (2003) 363 MR1975035
13	A Dessai, On the moduli space of nonnegatively curved metrics on Milnor spheres, preprint (2018) arXiv:1712.08821v2
14	A Dessai, D González-Álvaro, Moduli space of metrics of nonnegative sectional or positive Ricci curvature on homotopy real projective spaces, Trans. Amer. Math. Soc. 374 (2021) 1 MR4188176
15	A Dessai, S Klaus, W Tuschmann, Nonconnected moduli spaces of nonnegative sectional curvature metrics on simply connected manifolds, Bull. Lond. Math. Soc. 50 (2018) 96 MR3778547
16	S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Univ. Press (1990) MR1079726
17	D G Ebin, The manifold of Riemannian metrics, from: "Global analysis" (editors S S Chern, S Smale), Proc. Sympos. Pure Math. XIV–XVI, Amer. Math. Soc. (1970) 11 MR0267604
18	C Escher, W Ziller, Topology of non-negatively curved manifolds, Ann. Global Anal. Geom. 46 (2014) 23 MR3205800
19	H Geiges, C B Thomas, Contact topology and the structure of 5–manifolds with π₁ = Z₂, Ann. Inst. Fourier (Grenoble) 48 (1998) 1167 MR1656012
20	P B Gilkey, J Park, W Tuschmann, Invariant metrics of positive Ricci curvature on principal bundles, Math. Z. 227 (1998) 455 MR1612669
21	M J Goodman, On the moduli spaces of metrics with nonnegative sectional curvature, Ann. Global Anal. Geom. 57 (2020) 305 MR4070165
22	K Grove, W Ziller, Curvature and symmetry of Milnor spheres, Ann. of Math. 152 (2000) 331 MR1792298
23	K Grove, W Ziller, Cohomogeneity one manifolds with positive Ricci curvature, Invent. Math. 149 (2002) 619 MR1923478
24	K Grove, W Ziller, Lifting group actions and nonnegative curvature, Trans. Amer. Math. Soc. 363 (2011) 2865 MR2775790
25	I Hambleton, M Kreck, P Teichner, Nonorientable 4–manifolds with fundamental group of order 2, Trans. Amer. Math. Soc. 344 (1994) 649 MR1234481
26	I Hambleton, Y Su, On certain 5–manifolds with fundamental group of order 2, Q. J. Math. 64 (2013) 149 MR3032093
27	R C Kirby, L R Taylor, Pin structures on low-dimensional manifolds, from: "Geometry of low-dimensional manifolds, II" (editors S K Donaldson, C B Thomas), London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 177 MR1171915
28	M Kreck, S Stolz, A diffeomorphism classification of 7–dimensional homogeneous Einstein manifolds with SU(3) × SU(2) × U(1)–symmetry, Ann. of Math. 127 (1988) 373 MR0932303
29	M Kreck, S Stolz, Some nondiffeomorphic homeomorphic homogeneous 7–manifolds with positive sectional curvature, J. Differential Geom. 33 (1991) 465 MR1094466
30	M Kreck, S Stolz, Nonconnected moduli spaces of positive sectional curvature metrics, J. Amer. Math. Soc. 6 (1993) 825 MR1205446
31	H B Lawson Jr., M L Michelsohn, Spin geometry, 38, Princeton Univ. Press (1989) MR1031992
32	S López de Medrano, Involutions on manifolds, 59, Springer (1971) MR0298698
33	J C Nash, Positive Ricci curvature on fibre bundles, J. Differential Geometry 14 (1979) 241 MR0587552
34	G Perelman, Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers, from: "Comparison geometry" (editors K Grove, P Petersen), Math. Sci. Res. Inst. Publ. 30, Cambridge Univ. Press (1997) 157 MR1452872
35	L J Schwachhöfer, W Tuschmann, Metrics of positive Ricci curvature on quotient spaces, Math. Ann. 330 (2004) 59 MR2091679
36	C Searle, F Wilhelm, How to lift positive Ricci curvature, Geom. Topol. 19 (2015) 1409 MR3352240
37	J P Sha, D Yang, Positive Ricci curvature on the connected sums of Sⁿ × S^m, J. Differential Geom. 33 (1991) 127 MR1085137
38	J P Sha, D Yang, Positive Ricci curvature on compact simply connected 4–manifolds, from: "Differential geometry: Riemannian geometry, III" (editors R Greene, S T Yau), Proc. Sympos. Pure Math. 54, Amer. Math. Soc. (1993) 529 MR1216644
39	S Smale, On the structure of 5–manifolds, Ann. of Math. 75 (1962) 38 MR0141133
40	R E Stong, Relations among characteristic numbers, I, Topology 4 (1965) 267 MR0192515
41	M Y Wang, W Ziller, Einstein metrics on principal torus bundles, J. Differential Geom. 31 (1990) 215 MR1030671
42	J Wermelinger, Moduli space of metrics of nonnegative sectional or positive Ricci curvature on Brieskorn quotients in dimension 5, preprint (2020) arXiv:2006.13697
43	D Wraith, Exotic spheres with positive Ricci curvature, J. Differential Geom. 45 (1997) 638 MR1472892
44	D J Wraith, New connected sums with positive Ricci curvature, Ann. Global Anal. Geom. 32 (2007) 343 MR2346222
45	D J Wraith, On the moduli space of positive Ricci curvature metrics on homotopy spheres, Geom. Topol. 15 (2011) 1983 MR2860985