Artículos de revistas
G2–instantons Over Asymptotically Cylindrical Manifolds
Registro en:
Geometry And Topology. Mathematical Sciences Publishers, v. 19, n. 1, p. 61 - 111, 2015.
14653060
10.2140/gt.2015.19.61
2-s2.0-84924311213
Autor
Sa Earp H.N.
Institución
Resumen
A concrete model for a 7–dimensional gauge theory under special holonomy is proposed, within the paradigm of Donaldson and Thomas, over the asymptotically cylindrical G2 –manifolds provided by Kovalev’s solution to a noncompact version of the Calabi conjecture. One obtains a solution to the G2 –instanton equation from the associated Hermitian Yang–Mills problem, to which the methods of Simpson et al are applied, subject to a crucial asymptotic stability assumption over the “boundary at infinity”. 19 1 61 111 Baraglia, D., G2 Geometry and Integrable Systems, , PhD thesis, University of Oxford (2009) Available at arXiv:1002.1767v2 Barth, W.P., Some properties of stable rank-2 vector bundles on Pn (1977) Math. Ann, 226, pp. 125-150. , MR0429896 Wp Barth, K., Hulek, C., Peters, A., De Ven, (2004) Compact Complex Surfaces, , 2nd edition, Ergeb. Math. Grenzgeb. 4, Springer, MR2030225 Bryant, R.L., (1985) Metrics with Holonomy G2 Or Spin.7/, From: “Workshop Bonn 1984, pp. 269-277. , F Hirzebruch, J Schwermer, S Suter, editorsLecture Notes in Math. 1111, Springer, MR797426 Bryant, R.L., Salamon, S.M., On the construction of some complete metrics with exceptional holonomy (1989) Duke Math. J, 58, pp. 829-850. , MR1016448 Buttler, M., (1999) The Geometry of CR–manifolds, , PhD thesis, University of Oxford Donaldson, S.K., Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector bundles (1985) Proc. London Math. Soc., 50, pp. 1-26. , MR765366 Donaldson, S.K., Infinite determinants, stable bundles and curvature (1987) Duke Math. J, 54, pp. 231-247. , MR885784 Donaldson, S.K., The approximation of instantons (1993) Geom. Funct. Anal, 3, pp. 179-200. , MR1209301 Donaldson, S.K., (2002) Floer Homology Groups in Yang–Mills Theory, , Cambridge Tracts in Math. 147, Cambridge Univ. Press, MR1883043 Donaldson, S.K., Kronheimer, P.B., (1990) The Geometry of Four-Manifolds, , Oxford Univ. Press, MR1079726 Eells, J., Jr, J.H., Sampson, Harmonic mappings of Riemannian manifolds (1964) Amer. J. Math, 86, pp. 109-160. , MR0164306 Fernández, M., A Gray, Riemannian manifolds with structure group G2 (1982) Ann. Mat. Pura Appl, 132, pp. 19-45. , MR696037 Gilbarg, D., Trudinger, N.S., (2001) Elliptic Partial Differential Equations of Second Order, , Springer, MR1814364 Griffiths, P., Harris, J., (1994) Principles of Algebraic Geometry, , Wiley, New York, MR1288523 Grigoryan, A., Gaussian upper bounds for the heat kernel on arbitrary manifolds (1997) J. Differential Geom, 45, pp. 33-52. , MR1443330 Guo, G.-Y., Yang–Mills fields on cylindrical manifolds and holomorphic bundles, I, Comm (1996) Math. Phys, 179, pp. 737-775. , MR1400761 Hamilton, R.S., Harmonic maps of manifolds with boundary (1975) Lecture Notes in Math, 471. , Springer, Berlin, MR0482822 Huybrechts, D., (2005) Complex Geometry, , Springer, MR2093043 Jardim, M., Stable bundles on 3–fold hypersurfaces (2007) Bull. Braz. Math. Soc, 38, pp. 649-659. , MR2371952 Jardim, M.B., Earp, H.S., Monad Constructions of Asymptotically Stable Bundles, , in preparation Joyce, D.D., (2000) Compact Manifolds with Special Holonomy, , Oxford Univ. Press, MR1787733 Kovalev, A., Twisted connected sums and special Riemannian holonomy (2003) J. Reine Angew. Math., 565, pp. 125-160. , MR2024648 Kovalev, A., From Fano threefolds to compact G2 –manifolds, from: “Strings and geometry (2004) Clay Math. Proc. 3, Amer. Math. Soc, pp. 193-202. , MR2103723 Milnor, J.W., Stasheff, J.D., (1974) Characteristic Classes, , Annals of Math. Studies 76, Princeton Univ. Press, MR0440554 Moser, J., On Harnack’s theorem for elliptic differential equations (1961) Comm. Pure Appl.Math, 14, pp. 577-591. , MR0159138 Mukai, S., On the moduli space of bundles on K3 surfaces, I, from: “Vector bundles on algebraic varieties” (1987) Tata Inst. Fund. Res. Stud. Math., 11, pp. 341-413. , Tata Inst., Bombay, MR893604 Mukai, S., (1992) Fano 3–folds, From: “Complex Projective Geometry, pp. 255-263. , G Ellingsrud, C Peskine, G Sacchiero, SA Strømme, editorsLondon Math. Soc. Lecture Note Ser. 179, Cambridge Univ. Press, MR1201387 C Okonek, M., Schneider, H., Spindler, Vector bundles on complex projective spaces (1980) Progress in Math, 3. , Birkhäuser, MR561910 Rudin, W., (1976) Principles of Mathematical Analysis, , 3rd edition, McGraw–Hill, New York, MR0385023 HN Sá Earp, G2 –instantons over asymptotically cylindrical manifolds arXiv: 1101.0880HN Sá Earp, G2 –instantons over Kovalev manifolds, II, in preparation(2009), HN Sá Earp, Instantons on G2 –manifolds, PhD thesis, Imperial College LondonSalamon, S., Riemannian geometry and holonomy groups (1989) Pitman Res. Notes Math, 201. , Longman, Harlow, UK, MR1004008 Simpson, C.T., Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization (1988) J. Amer. Math. Soc, 1, pp. 867-918. , MR944577 Taubes, C.H., Metrics, connections and gluing theorems (1996) CBMS Regional Conf. Series in Math. 89, Amer. Math. Soc, , MR1400226 Thomas, R., (1997) Gauge Theory on Calabi–Yau Manifolds, , PhD thesis, Univeristy of Oxford Walpuski, T., (2012) G2 –instantons on Generalised Kummer Constructions, , arXiv: 1109.6609v2