Geometry & Topology Volume 23, issue 7 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Toric geometry of $\mathrm{G}_2$–manifolds

Thomas Bruun Madsen and Andrew Swann

Geometry & Topology 23 (2019) 3459–3500

DOI: 10.2140/gt.2019.23.3459

Bibliography

1	M Aganagic, A Klemm, M Mariño, C Vafa, The topological vertex, Comm. Math. Phys. 254 (2005) 425 MR2117633
2	V Apostolov, S Salamon, Kähler reduction of metrics with holonomy G₂, Comm. Math. Phys. 246 (2004) 43 MR2044890
3	D Baraglia, Moduli of coassociative submanifolds and semi-flat G₂–manifolds, J. Geom. Phys. 60 (2010) 1903 MR2735277
4	R J Baston, M G Eastwood, The Penrose transform : its interaction with representation theory, Clarendon (1989) MR1038279
5	Y V Bazaikin, O A Bogoyavlenskaya, Complete Riemannian metrics with holonomy group G₂ on deformations of cones over S³ × S³, Mat. Zametki 93 (2013) 645 MR3206014
6	M Berger, Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France 83 (1955) 279 MR79806
7	A L Besse, Einstein manifolds, 10, Springer (1987) MR867684
8	R Bielawski, Complete hyper–Kähler 4n–manifolds with a local tri-Hamiltonian ℝⁿ–action, Math. Ann. 314 (1999) 505 MR1704547
9	S Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946) 776 MR18022
10	O A Bogoyavlenskaya, On a new family of complete Riemannian metrics on S³ × ℝ⁴ with holonomy group G₂, Sibirsk. Mat. Zh. 54 (2013) 551 MR3112613
11	A Brandhuber, J Gomis, S S Gubser, S Gukov, Gauge theory at large N and new G₂ holonomy metrics, Nuclear Phys. B 611 (2001) 179 MR1857379
12	R L Bryant, Metrics with exceptional holonomy, Ann. of Math. 126 (1987) 525 MR916718
13	R L Bryant, S M Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Math. J. 58 (1989) 829 MR1016448
14	R Chihara, G₂–metrics arising from non-integrable special Lagrangian fibrations, Complex Manifolds 6 (2019) 348 MR3987861
15	D Conti, T B Madsen, Invariant torsion and G₂–metrics, Complex Manifolds 2 (2015) 140 MR3420324
16	V Cortés, X Han, T Mohaupt, Completeness in supergravity constructions, Comm. Math. Phys. 311 (2012) 191 MR2892468
17	A Dancer, A Swann, Hypertoric manifolds and hyperkähler moment maps, from: "Special metrics and group actions in geometry" (editors S. Chiossi, A. Fino, E. Musso, F. Podestà, L. Vezzoni), Springer INdAM Ser. 23, Springer (2017) 107 MR3751964
18	G. Dinca, J. Mawhin, Brouwer degree and applications, book project (2009)
19	K Dixon, The multi-moment maps of the nearly Kähler S³ × S³, Geom. Dedicata 200 (2019) 351 MR3956200
20	S Donaldson, Adiabatic limits of co-associative Kovalev–Lefschetz fibrations, from: "Algebra, geometry, and physics in the 21st century" (editors D Auroux, L Katzarkov, T Pantev, Y Soibelman, Y Tschinkel), Progr. Math. 324, Springer (2017) 1 MR3702382
21	M Eastwood, A complex from linear elasticity, from: "The proceedings of the 19th winter school Geometry and Physics", Rend. Circ. Mat. Palermo Suppl. 63, Circolo Matematico di Palermo (2000) 23 MR1758075
22	M Eastwood, Ricci curvature and the mechanics of solids, Austral. Math. Soc. Gaz. 37 (2010) 238 MR2730448
23	M Fernández, A Gray, Riemannian manifolds with structure group G₂, Ann. Mat. Pura Appl. 132 (1982) 19 MR696037
24	J Fine, C Yao, Hypersymplectic 4-manifolds, the G₂–Laplacian flow, and extension assuming bounded scalar curvature, Duke Math. J. 167 (2018) 3533 MR3881202
25	L Foscolo, M Haskins, J Nordström, Complete non-compact G₂–manifolds from asymptotically conical Calabi–Yau 3–folds, preprint (2017) arXiv:1709.04904
26	L Foscolo, M Haskins, J Nordström, Infinitely many new families of complete cohomogeneity one G₂–manifolds : G₂ analogues of the Taub–NUT and Eguchi–Hanson spaces, preprint (2018) arXiv:1805.02612
27	G Gibbons, S Hawking, Gravitational multi-instantons, Phys. Lett. B 78 (1978) 430
28	G W Gibbons, S W Hawking, Classification of gravitational instanton symmetries, Comm. Math. Phys. 66 (1979) 291 MR535152
29	R Harvey, H B Lawson Jr., Calibrated geometries, Acta Math. 148 (1982) 47 MR666108
30	M J Hughes, E Swartz, Quotients of spheres by linear actions of tori, preprint (2012) arXiv:1205.6387
31	M Ionel, M Min-Oo, Cohomogeneity one special Lagrangian 3–folds in the deformed and the resolved conifolds, Illinois J. Math. 52 (2008) 839 MR2546011
32	Y Karshon, E Lerman, Non-compact symplectic toric manifolds, Symmetry Integrability Geom. Methods Appl. 11 (2015) MR3371718
33	S Kobayashi, Transformation groups in differential geometry, 70, Springer (1972) MR0355886
34	J Li, C C M Liu, K Liu, J Zhou, A mathematical theory of the topological vertex, Geom. Topol. 13 (2009) 527 MR2469524
35	I Madsen, J Tornehave, From calculus to cohomology: de Rham cohomology and characteristic classes, Cambridge Univ. Press (1997) MR1454127
36	T B Madsen, A Swann, Multi-moment maps, Adv. Math. 229 (2012) 2287 MR2880222
37	T B Madsen, A Swann, Closed forms and multi-moment maps, Geom. Dedicata 165 (2013) 25 MR3079342
38	J N Mather, Differentiable invariants, Topology 16 (1977) 145 MR436204
39	J Mawhin, A simple approach to Brouwer degree based on differential forms, Adv. Nonlinear Stud. 4 (2004) 535 MR2100911
40	G W Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975) 63 MR370643
41	M B Stenzel, Ricci-flat metrics on the complexification of a compact rank one symmetric space, Manuscripta Math. 80 (1993) 151 MR1233478
42	A F Swann, Twists versus modifications, Adv. Math. 303 (2016) 611 MR3552535
43	A F Swann, Moment maps and toric special holonomy, talk slides (2017)
44	A F Swann, Toric geometry of G₂–metrics, talk slides (2018)
45	R Szőke, Complex structures on tangent bundles of Riemannian manifolds, Math. Ann. 291 (1991) 409 MR1133340