메뉴 건너뛰기




Volumn 49, Issue 2, 1998, Pages 265-410

PU(2) monopoles. I: Regularity, uhlenbeck compactness, and transversality

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0009202284     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214461020     Document Type: Article
Times cited : (46)

References (99)
  • 2
    • 0003796630 scopus 로고
    • Academic Press, Orlando, FL
    • R. A. Adams, Sobolev spaces, Academic Press, Orlando, FL, 1975.
    • (1975) Sobolev Spaces
    • Adams, R.A.1
  • 3
    • 0346101129 scopus 로고
    • Unicité et convexité dans les problèmes différentiels
    • Univ. of Montreal Press
    • S. Agmon, Unicité et convexité dans les problèmes différentiels, Sém. Math. Sup., 1965, Univ. of Montreal Press, 1966.
    • (1965) Sém. Math. Sup.
    • Agmon, S.1
  • 4
    • 84981761614 scopus 로고
    • Lower bounds and uniqueness theorems for solutions of differential equations in Hilbert spaces
    • S. Agmon & L. Nirenberg, Lower bounds and uniqueness theorems for solutions of differential equations in Hilbert spaces, Comm. Pure Appl. Math. 20 (1967) 207-229.
    • (1967) Comm. Pure Appl. Math , vol.20 , pp. 207-229
    • Agmon, S.1    Nirenberg, L.2
  • 5
    • 0001104071 scopus 로고
    • A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of the second order
    • N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of the second order, J. Math. Pures Appl. 36 (1957) 235-249.
    • (1957) J. Math. Pures Appl , vol.36 , pp. 235-249
    • Aronszajn, N.1
  • 9
    • 0000120329 scopus 로고
    • Moduli of stable pairs for holomorphic bundles over Riemann surfaces
    • S. B. Bradlow & G. D. Daskalopoulos, Moduli of stable pairs for holomorphic bundles over Riemann surfaces, Internat. J. Math. 2 (1991) 477-513.
    • (1991) Internat. J. Math , vol.2 , pp. 477-513
    • Bradlow, S.B.1    Daskalopoulos, G.D.2
  • 10
    • 0040847564 scopus 로고    scopus 로고
    • Non-abelian monopoles and vortices
    • Aarhus, 1995, Lecture Notes in Pure and Appl. Math. 184, Dekker, New York, alg-geom/9602010
    • S. B. Bradlow & O. Garcia-Prada, Non-abelian monopoles and vortices, Proc. Conference on Geom. and Phys. (Aarhus, 1995), Lecture Notes in Pure and Appl. Math. 184, Dekker, New York, 1997, 567-589; alg-geom/9602010.
    • (1997) Proc. Conference on Geom. And Phys , pp. 567-589
    • Bradlow, S.B.1    Garcia-Prada, O.2
  • 14
    • 84972508273 scopus 로고
    • An application of gauge theory to four-dimensional topology
    • S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279-315.
    • (1983) J. Differential Geom , vol.18 , pp. 279-315
    • Donaldson, S.K.1
  • 15
    • 84972564405 scopus 로고
    • Connections, cohomology and the intersection forms of four-manifolds
    • S. K. Donaldson, Connections, cohomology and the intersection forms of four-manifolds, J. Differential Geom. 24 (1986) 275-341.
    • (1986) J. Differential Geom , vol.24 , pp. 275-341
    • Donaldson, S.K.1
  • 16
    • 84972517053 scopus 로고
    • Irrationality and the h-cobordism conjecture
    • S. K. Donaldson, Irrationality and the h-cobordism conjecture, J. Differential Geom. 26 (1987), 141-168.
    • (1987) J. Differential Geom , vol.26 , pp. 141-168
    • Donaldson, S.K.1
  • 17
    • 84972514117 scopus 로고
    • The orientation of Yang-Mills moduli spaces and f-manifold topology
    • S. K. Donaldson, The orientation of Yang-Mills moduli spaces and f-manifold topology, J. Differential Geom. 26 (1987) 397-428.
    • (1987) J. Differential Geom , vol.26 , pp. 397-428
    • Donaldson, S.K.1
  • 18
    • 28744452988 scopus 로고
    • Polynomial invariants for smooth four-manifolds
    • S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990) 257-315.
    • (1990) Topology , vol.29 , pp. 257-315
    • Donaldson, S.K.1
  • 19
    • 0030538381 scopus 로고    scopus 로고
    • The Seiberg- Witten equations and four-manifold topology
    • S. K. Donaldson, The Seiberg- Witten equations and four-manifold topology, Bull. Amer. Math. Soc. 33 (1996) 45-70.
    • (1996) Bull. Amer. Math. Soc , vol.33 , pp. 45-70
    • Donaldson, S.K.1
  • 24
    • 0000662479 scopus 로고
    • PU(2) monopoles and relations between four-manifold invariants
    • dg-ga/9709022
    • P. M. N. Feehan & T. G. Leness, PU(2) monopoles and relations between four-manifold invariants, Topology Appl. 88 (1988) 111-145; dg-ga/9709022.
    • (1988) Topology Appl. , vol.88 , pp. 111-145
    • Feehan, P.M.N.1    Leness, T.G.2
  • 28
    • 0029681299 scopus 로고
    • Donaldson invariants of 4-manifolds with simple type
    • R. Fintushel & R. Stern, Donaldson invariants of 4-manifolds with simple type, J. Differential Geom. 42 (1995) 577-633.
    • (1995) J. Differential Geom , vol.42 , pp. 577-633
    • Fintushel, R.1    Stern, R.2
  • 29
    • 1542555328 scopus 로고
    • An instanton-invariant for 3-manifolds
    • A. Floer, An instanton-invariant for 3-manifolds, Comm. Math. Phys. 118 (1988) 215-240.
    • (1988) Comm. , vol.118 , pp. 215-240
    • Floer, A.1
  • 32
    • 0002066831 scopus 로고
    • Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces
    • R. Friedman & Z. Qin, Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces, Comm. Anal. Geom. (1995) 11-83.
    • (1995) Comm. Anal. Geom , pp. 11-83
    • Friedman, R.1    Qin, Z.2
  • 35
    • 0039738851 scopus 로고    scopus 로고
    • Modular forms and Donaldson invariants for 4-manifolds withb+ = 1
    • + = 1, J. Amer. Math. Soc. 9 (1996), 827-843.
    • (1996) J. Amer. Math. Soc , vol.9 , pp. 827-843
    • Göttsche, L.1
  • 42
    • 84990569674 scopus 로고
    • Unique continuation in geometry
    • J. Kazdan, Unique continuation in geometry, Comm. Pure Appl. Math. 41 (1988) 667-681.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 667-681
    • Kazdan, J.1
  • 47
    • 0001278369 scopus 로고
    • The genus of embedded surfaces in the projective plane
    • P. B. Kronheimer & T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994) 797-808.
    • (1994) Math. Res. Lett , vol.1 , pp. 797-808
    • Kronheimer, P.B.1    Mrowka, T.S.2
  • 48
    • 84972530014 scopus 로고
    • Embedded surfaces and the structure of Donaldson’s polynomial invariants
    • P. B. Kronheimer & T. S. Mrowka, Embedded surfaces and the structure of Donaldson’s polynomial invariants, J. Differential Geom. 43 (1995) 573-734.
    • (1995) J. Differential Geom , vol.43 , pp. 573-734
    • Kronheimer, P.B.1    Mrowka, T.S.2
  • 49
    • 0031502381 scopus 로고    scopus 로고
    • Monopoles and contact structures
    • P. B. Kronheimer & T. S. Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209-255.
    • (1997) Invent. Math , vol.130 , pp. 209-255
    • Kronheimer, P.B.1    Mrowka, T.S.2
  • 50
    • 0031556451 scopus 로고    scopus 로고
    • Mathai-Quillen formulation of twisted N=f su-persymmetric Gauge theories in four dimensions
    • J. M. F. Labastida & C. Lozano, Mathai-Quillen formulation of twisted N=f su-persymmetric Gauge theories in four dimensions, Nuclear Phys. B 502 (1997) 741-790; hep-th/9702106.
    • (1997) Nuclear Phys. B , vol.502 , pp. 741-790
    • Labastida, J.M.F.1    Lozano, C.2
  • 51
    • 0000641504 scopus 로고
    • Non-abelian monopoles on four-manifolds
    • J. M. F. Labastida & M. Marino, Non-abelian monopoles on four-manifolds, Nuclear Phys. B 448 (1995) 373-395; hep-th/9504010.
    • (1995) Nuclear Phys. B , vol.448 , pp. 373-395
    • Labastida, J.M.F.1    Marino, M.2
  • 52
    • 0001479017 scopus 로고
    • Polynomial invariants for SU(2) monopoles
    • J. M. F. Labastida & M. Marino, Polynomial invariants for SU(2) monopoles, Nuclear Phys. B 456 (1995) 633-668; hep-th/9507140.
    • (1995) Nuclear Phys. B , vol.456 , pp. 633-668
    • Labastida, J.M.F.1    Marino, M.2
  • 53
    • 0031116530 scopus 로고    scopus 로고
    • Twisted N = 2 supersymmetry with central charge and equivariant cohomology
    • J. M. F. Labastida & M. Marino, Twisted N = 2 supersymmetry with central charge and equivariant cohomology, Comm. Math. Phys. 185 (1997) 37-71; hepth/9603169.
    • (1997) Comm. Math. Phys. , vol.185 , pp. 37-71
    • Labastida, J.M.F.1    Marino, M.2
  • 56
    • 0003271068 scopus 로고
    • The theory of gauge fields in four dimensions
    • Providence, RI
    • H. B. Lawson, The theory of gauge fields in four dimensions, Conf. Board Math. Sci. 58, Amer. Math. Soc., Providence, RI, 1985.
    • (1985) Conf. Board Math. Sci , vol.58
    • Lawson, H.B.1
  • 58
    • 85037904311 scopus 로고    scopus 로고
    • Donaldson wall-crossing formulas via topology
    • to appear; dg-ga/9603016
    • T. G. Leness, Donaldson wall-crossing formulas via topology, Forum Math., to appear; dg-ga/9603016.
    • Forum Math.
    • Leness, T.G.1
  • 60
    • 0001150307 scopus 로고    scopus 로고
    • Integration over the u-plane in Donaldson theory
    • G. Moore & E. Witten, Integration over the u-plane in Donaldson theory, Adv. Theor. Math. Phys. 1 (1997) 298-387; hep-th/9709193.
    • (1997) Adv. Theor. Math. Phys. , vol.1 , pp. 298-387
    • Moore, G.1    Witten, E.2
  • 66
    • 0347108812 scopus 로고    scopus 로고
    • Seiberg-Witten monopoles on Seifert-fibered spaces
    • T. S. Mrowka, P. S. Ozsväth & B. Yu, Seiberg-Witten monopoles on Seifert-fibered spaces, Comm. Anal. Geom. 5 (1997) 685-791.
    • (1997) Comm. Anal. Geom , vol.5 , pp. 685-791
    • Mrowka, T.S.1    Ozsväth, P.S.2    Yu, B.3
  • 67
    • 21844488591 scopus 로고
    • The coupled Seiberg-Witten equations, vortices, and moduli spaces of stable pairs
    • alg-geom/9505012
    • C. Okonek & A. Teleman, The coupled Seiberg-Witten equations, vortices, and moduli spaces of stable pairs, Internat. J. Math. 6 (1995) 893-910; alg-geom/9505012.
    • (1995) Internat. J. Math. , vol.6 , pp. 893-910
    • Okonek, C.1    Teleman, A.2
  • 68
    • 0030487274 scopus 로고    scopus 로고
    • Quaternionic monopoles
    • C. Okonek & A. Teleman, Quaternionic monopoles, Comm. Math. Phys. 180 (1996) 363-388; alg-geom/9505029.
    • (1996) Comm. Math. Phys. , vol.180 , pp. 363-388
    • Okonek, C.1    Teleman, A.2
  • 70
    • 34250225548 scopus 로고
    • Gauge theories on four dimensional Riemannian manifolds
    • T. H. Parker, Gauge theories on four dimensional Riemannian manifolds, Comm. Math. Phys. 85 (1982) 563-602.
    • (1982) Comm. Math. Phys , vol.85 , pp. 563-602
    • Parker, T.H.1
  • 73
    • 0011045994 scopus 로고
    • Invariants of the smooth structure of an algebraic surface arising from the Dirac operator
    • V. Y. Pidstrigach & A. N. Tyurin, Invariants of the smooth structure of an algebraic surface arising from the Dirac operator, Russian Acad. Sei. Izv. Math. 40 (1993) 267-351.
    • (1993) Russian Acad. Sei. Izv. Math , vol.40 , pp. 267-351
    • Pidstrigach, V.Y.1    Tyurin, A.N.2
  • 78
    • 0001185311 scopus 로고
    • A direct method for mimizing the Yang-Mills functional
    • S. Sedlacek, A direct method for mimizing the Yang-Mills functional, Comm. Math. Phys. 86 (1982) 515-527.
    • (1982) Comm. Math. Phys , vol.86 , pp. 515-527
    • Sedlacek, S.1
  • 80
    • 0013198798 scopus 로고
    • An infinite-dimensional version of Sard’s theorem
    • S. Smale, An infinite-dimensional version of Sard’s theorem., Amer. J. Math. 87 (1973) 213-221.
    • (1973) Amer. J. Math , vol.87 , pp. 213-221
    • Smale, S.1
  • 81
    • 84972491713 scopus 로고
    • Self-dual Yang-Mills connections on non-self-dual f-manifolds
    • C. H. Taubes, Self-dual Yang-Mills connections on non-self-dual f-manifolds, J. Differential Geom. 17 (1982) 139-170.
    • (1982) J. Differential Geom , vol.17 , pp. 139-170
    • Taubes, C.H.1
  • 82
    • 84972545621 scopus 로고
    • Self-dual connections on f-manifolds with indefinite intersection matrix
    • C. H. Taubes, Self-dual connections on f-manifolds with indefinite intersection matrix, J. Differential Geom. 19 (1984) 517-560.
    • (1984) J. Differential Geom , vol.19 , pp. 517-560
    • Taubes, C.H.1
  • 83
    • 84972496576 scopus 로고
    • Path-connected Yang-Mills moduli spaces
    • C. H. Taubes, Path-connected Yang-Mills moduli spaces, J. Differential Geom. 19 (1984) 337-392.
    • (1984) J. Differential Geom , vol.19 , pp. 337-392
    • Taubes, C.H.1
  • 84
    • 0000016538 scopus 로고
    • A framework for Morse theory for the Yang-Mills functional
    • C. H. Taubes, A framework for Morse theory for the Yang-Mills functional, Invent. Math. 94 (1988) 327-402.
    • (1988) Invent. Math , vol.94 , pp. 327-402
    • Taubes, C.H.1
  • 85
    • 84972528305 scopus 로고
    • The stable topology of self-dual moduli spaces
    • C. H. Taubes, The stable topology of self-dual moduli spaces, J. Differential Geom. 29 (1989) 162-230.
    • (1989) J. Differential Geom , vol.29 , pp. 162-230
    • Taubes, C.H.1
  • 86
    • 84972521544 scopus 로고
    • Casson’s invariant and gauge theory
    • C. H. Taubes, Casson’s invariant and gauge theory, J. Differential Geom. 31 (1990) 547-599.
    • (1990) J. Differential Geom , vol.31 , pp. 547-599
    • Taubes, C.H.1
  • 88
    • 0039463144 scopus 로고
    • Unique continuation theorems in qauge theories
    • C. H. Taubes, Unique continuation theorems in qauge theories, Comm. Anal. Geom. 2 (1994) 35-52.
    • (1994) Comm. Anal. Geom , vol.2 , pp. 35-52
    • Taubes, C.H.1
  • 89
    • 0000368324 scopus 로고
    • The Seiberg-Witten invariants and symplectic forms
    • C. H. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809-822.
    • (1994) Math. Res. Lett , vol.1 , pp. 809-822
    • Taubes, C.H.1
  • 91
    • 0031287289 scopus 로고    scopus 로고
    • Non-abelian Seiberg-Witten theory and stable oriented pairs
    • alg-geom/9609020
    • A. Teleman, Non-abelian Seiberg-Witten theory and stable oriented pairs, Internat. J. Math. 8 (1997) 507-535; alg-geom/9609020.
    • (1997) Internat. J. Math. , vol.8 , pp. 507-535
    • Teleman, A.1
  • 93
    • 85037888861 scopus 로고    scopus 로고
    • Untitled preprint
    • A. Teleman, Untitled preprint.
    • Teleman, A.1
  • 94
    • 0001830025 scopus 로고
    • Removable singularities in Yang-Mills fields
    • K. K. Uhlenbeck, Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982) 11-29.
    • (1982) Comm. Math. Phys , vol.83 , pp. 11-29
    • Uhlenbeck, K.K.1
  • 95
    • 34250242066 scopus 로고
    • Connections with Lp bounds on curvature
    • p bounds on curvature, Comm. Math. Phys. 83 (1982) 31-42.
    • (1982) Comm. Math. Phys , vol.83 , pp. 31-42
    • Uhlenbeck, K.K.1
  • 96
    • 0039030154 scopus 로고
    • The Chern classes of Sobolev connections
    • K. K. Uhlenbeck, The Chern classes of Sobolev connections, Comm. Math. Phys. 101 (1985) 449-457.
    • (1985) Comm. Math. Phys , vol.101 , pp. 449-457
    • Uhlenbeck, K.K.1
  • 98
    • 0000368321 scopus 로고
    • Monopoles and four-manifolds
    • E. Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769-796.
    • (1994) Math. Res. Lett , vol.1 , pp. 769-796
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.