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Volumn 12, Issue 2, 2008, Pages 747-918

Instanton Floer homology with Lagrangian boundary conditions

Author keywords

3 manifold with boundary; Atiyah floer conjecture

Indexed keywords


EID: 74249117777     PISSN: 13640380     EISSN: 13640380     Source Type: Journal    
DOI: 10.2140/gt.2008.12.747     Document Type: Article
Times cited : (41)

References (37)
  • 1
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions
    • MR 0125307 Zbl 0093.10401
    • S Agmon, A Douglis, L Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959) 623-727 MR 0125307 Zbl 0093.10401
    • (1959) I, Comm. Pure Appl. Math , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 84981761614 scopus 로고
    • Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space
    • MR 0204829 Zbl 0147.34603
    • S Agmon, L Nirenberg, Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space, Comm. Pure Appl. Math. 20 (1967) 207-229 MR 0204829 Zbl 0147.34603
    • (1967) Comm. Pure Appl. Math , vol.20 , pp. 207-229
    • Agmon, S.1    Nirenberg, L.2
  • 3
    • 0001502193 scopus 로고
    • New invariants of 3-and 4-dimensional manifolds, from: The mathematical heritage of Hermann Weyl (Durham, NC, 1987)
    • (editor R. Wells), MR 974342 Zbl 0667.57018
    • M F Atiyah, New invariants of 3-and 4-dimensional manifolds, from: The mathematical heritage of Hermann Weyl (Durham, NC, 1987) (editor R. Wells), Proc. Sympos. Pure Math. 48, Amer. Math. Soc. (1988) 285-299 MR 974342 Zbl 0667.57018
    • (1988) Proc. Sympos. Pure Math. Amer. Math. Soc , vol.48 , pp. 285-299
    • Atiyah, M.F.1
  • 4
    • 0000979746 scopus 로고
    • The Yang-Mills equations over Riemann surfaces
    • MR 702806 Zbl 0509.14014
    • M F Atiyah, R Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523-615 MR 702806 Zbl 0509.14014
    • (1983) Philos. Trans. Roy. Soc. London Ser. A , vol.308 , pp. 523-615
    • Atiyah, M.F.1    Bott, R.2
  • 7
    • 1342344570 scopus 로고    scopus 로고
    • The Maslov index: A functional analytical definition and the spectral flow formula
    • MR 1630119 Zbl 0932.37063
    • B Booss-Bavnbek, K Furutani, The Maslov index: a functional analytical definition and the spectral flow formula, Tokyo J. Math. 21 (1998) 1-34 MR 1630119 Zbl 0932.37063
    • (1998) Tokyo J. Math , vol.21 , pp. 1-34
    • Booss-Bavnbek, B.1    Furutani, K.2
  • 9
    • 84972514117 scopus 로고
    • The orientation of Yang-Mills moduli spaces and 4-manifold topology
    • MR 910015 Zbl 0683.57005
    • S K Donaldson, The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. Differential Geom. 26 (1987) 397-428 MR 910015 Zbl 0683.57005
    • (1987) J. Differential Geom , vol.26 , pp. 397-428
    • Donaldson, S.K.1
  • 10
    • 0038524923 scopus 로고    scopus 로고
    • Floer homology groups in Yang-Mills theory
    • Cambridge University Press, MR 1883043 Zbl 0998.53057
    • S K Donaldson, Floer homology groups in Yang-Mills theory, Cambridge Tracts in Mathematics 147, Cambridge University Press (2002) MR 1883043 Zbl 0998.53057
    • (2002) Cambridge Tracts In Mathematics , vol.147
    • Donaldson, S.K.1
  • 12
    • 0000159109 scopus 로고
    • Selfdual instantons and holomorphic curves
    • MR 1283871 Zbl 0812.58031
    • S Dostoglou, D A Salamon, Selfdual instantons and holomorphic curves, Ann. of Math. (2) 139 (1994) 581-640 MR 1283871 Zbl 0812.58031
    • (1994) Ann. of Math , vol.139 , Issue.2 , pp. 581-640
    • Dostoglou, S.1    Salamon, D.A.2
  • 14
    • 1542555328 scopus 로고
    • An instantoninvariant for 3-manifolds
    • MR 956166 Zbl 0684.53027
    • A Floer, An instantoninvariant for 3-manifolds, Comm. Math. Phys. 118 (1988) 215-240 MR 956166 Zbl 0684.53027
    • (1988) Comm. Math. Phys , vol.118 , pp. 215-240
    • Floer, A.1
  • 17
    • 0003612981 scopus 로고
    • Theorems and problems in functional analysis
    • Springer, MR 671088 Zbl 0486.46002
    • A A Kirillov, A D Gvishiani, Theorems and problems in functional analysis, Problem Books in Mathematics, Springer (1982) MR 671088 Zbl 0486.46002
    • (1982) Problem Books In Mathematics
    • Kirillov, A.A.1    Gvishiani, A.D.2
  • 18
    • 2942689754 scopus 로고    scopus 로고
    • The n-invariant, Maslov index, and spectral flow for Diractype operators on manifolds with boundary
    • MR 2044028 Zbl 1082.58021
    • P Kirk, M Lesch, The n-invariant, Maslov index, and spectral flow for Diractype operators on manifolds with boundary, Forum Math. 16 (2004) 553-629 MR 2044028 Zbl 1082.58021
    • (2004) Forum Math. , vol.16 , pp. 553-629
    • Kirk, P.1    Lesch, M.2
  • 19
    • 34547295040 scopus 로고    scopus 로고
    • Fourmanifold invariants from higherrank bundles
    • MR 2192061 Zbl 05033786
    • P B Kronheimer, Fourmanifold invariants from higherrank bundles, J. Differential Geom. 70 (2005) 59-112 MR 2192061 Zbl 05033786
    • (2005) J. Differential Geom , vol.70 , pp. 59-112
    • Kronheimer, P.B.1
  • 20
  • 22
    • 0004268695 scopus 로고
    • Based on notes by David W. Weaver, The University Press of Virginia, Charlottesville, Va, MR 0226651 Zbl 0136.20402
    • J W Milnor, Topology from the differentiable viewpoint, Based on notes by David W. Weaver, The University Press of Virginia, Charlottesville, Va. (1965) MR 0226651 Zbl 0136.20402
    • (1965) Topology From the Differentiable Viewpoint
    • Milnor, J.W.1
  • 25
    • 0000155326 scopus 로고
    • The Maslov index for paths
    • MR 1241874 Zbl 0798.58018
    • J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827-844 MR 1241874 Zbl 0798.58018
    • (1993) Topology , vol.32 , pp. 827-844
    • Robbin, J.1    Salamon, D.2
  • 26
    • 84953403020 scopus 로고
    • The spectral flow and the Maslov index
    • MR 1331677 Zbl 0859.58025
    • J Robbin, D Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995) 1-33 MR 1331677 Zbl 0859.58025
    • (1995) Bull. London Math. Soc , vol.27 , pp. 1-33
    • Robbin, J.1    Salamon, D.2
  • 29
    • 0013198076 scopus 로고    scopus 로고
    • Lectures on Floer homology, from: Symplectic geometry and topology (Park City, UT, 1997)
    • MR 1702944 Zbl 1031.53118
    • D Salamon, Lectures on Floer homology, from: Symplectic geometry and topology (Park City, UT, 1997), IAS/Park City Math. Ser. 7, Amer. Math. Soc. (1999) 143-229 MR 1702944 Zbl 1031.53118
    • (1999) Ias/park City Math. Ser. Amer. Math. Soc , vol.7 , pp. 143-229
    • Salamon, D.1
  • 30
    • 84972521544 scopus 로고
    • Casson's invariant and gauge theory
    • MR 1037415 Zbl 0702.53017
    • C H Taubes, Casson's invariant and gauge theory, J. Differential Geom. 31 (1990) 547-599 MR 1037415 Zbl 0702.53017
    • (1990) J. Differential Geom , vol.31 , pp. 547-599
    • Taubes, C.H.1
  • 31
    • 0039463144 scopus 로고
    • Unique continuation theorems in gauge theories
    • MR 1312676 Zbl 0838.53028
    • C H Taubes, Unique continuation theorems in gauge theories, Comm. Anal. Geom. 2 (1994) 35-52 MR 1312676 Zbl 0838.53028
    • (1994) Comm. Anal. Geom , vol.2 , pp. 35-52
    • Taubes, C.H.1
  • 32
    • 34250242066 scopus 로고
    • Connections with Lp bounds on curvature
    • MR 648356 Zbl 0499.58019
    • K K Uhlenbeck, Connections with Lp bounds on curvature, Comm. Math. Phys. 83 (1982) 31-42 MR 648356 Zbl 0499.58019
    • (1982) Comm. Math. Phys , vol.83 , pp. 31-42
    • Uhlenbeck, K.K.1
  • 33
    • 12944251849 scopus 로고    scopus 로고
    • Banach space valued Cauchy-Riemann equations with totally real boundary conditions
    • MR 2078416 Zbl 1083.53086
    • K Wehrheim, Banach space valued Cauchy-Riemann equations with totally real boundary conditions, Commun. Contemp. Math. 6 (2004) 601-635 MR 2078416 Zbl 1083.53086
    • (2004) Commun. Contemp. Math , vol.6 , pp. 601-635
    • Wehrheim, K.1
  • 35
    • 12944265394 scopus 로고    scopus 로고
    • Antiselfdual instantons with Lagrangian boundary conditions. I. Elliptic theory
    • MR 2116738 Zbl 1083.53029
    • K Wehrheim, Antiselfdual instantons with Lagrangian boundary conditions. I. Elliptic theory, Comm. Math. Phys. 254 (2005) 45-89 MR 2116738 Zbl 1083.53029
    • (2005) Comm. Math. Phys , vol.254 , pp. 45-89
    • Wehrheim, K.1
  • 36
    • 22544461677 scopus 로고    scopus 로고
    • Antiselfdual instantons with Lagrangian boundary conditions. II. Bubbling
    • MR 2171696 Zbl 1088.53013
    • K Wehrheim, Antiselfdual instantons with Lagrangian boundary conditions. II. Bubbling, Comm. Math. Phys. 258 (2005) 275-315 MR 2171696 Zbl 1088.53013
    • (2005) Comm. Math. Phys , vol.258 , pp. 275-315
    • Wehrheim, K.1
  • 37
    • 74249096496 scopus 로고    scopus 로고
    • Lagrangian boundary conditions for antiselfdual instantons and the Atiyah-Floer conjecture, Conference on Symplectic Topology
    • MR 2235859 Zbl 1129.53063
    • K Wehrheim, Lagrangian boundary conditions for antiselfdual instantons and the Atiyah-Floer conjecture, Conference on Symplectic Topology, J. Symplectic Geom. 3 (2005) 703-747 MR 2235859 Zbl 1129.53063
    • (2005) J. Symplectic Geom , vol.3 , pp. 703-747
    • Wehrheim, K.1


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