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Volumn 5, Issue , 2001, Pages 143-226

Gauge theoretic invariants of Dehn surgeries on knots

Author keywords

3 manifold invariants; Gauge theory; Homology 3 sphere; Maslov index; Spectral flow

Indexed keywords


EID: 0001190216     PISSN: 14653060     EISSN: None     Source Type: Journal    
DOI: 10.2140/gt.2001.5.143     Document Type: Article
Times cited : (15)

References (35)
  • 1
    • 0003406056 scopus 로고
    • Casson's invariant for oriented homology 3-spheres, an exposition
    • Princeton University Press
    • S Akbulut, J McCarthy, Casson's invariant for oriented homology 3-spheres, an exposition, Mathematical Notes no. 36, Princeton University Press (1990)
    • (1990) Mathematical Notes No. 36
    • Akbulut, S.1    McCarthy, J.2
  • 2
    • 4344636316 scopus 로고    scopus 로고
    • A topological method to compute spectral flow
    • D Auckly, A topological method to compute spectral flow, Kyungpook Math. J. 38 (1998) 181-203
    • (1998) Kyungpook Math. J. , vol.38 , pp. 181-203
    • Auckly, D.1
  • 3
    • 84989221068 scopus 로고
    • Spectral asymmetry and Riemannian geometry. I,II,III
    • M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry. I,II,III, Math. Proc. Camb. Phil. Soc. 77 (1975) 43-69; 78 (1975) 405-432; 79 (1976) 71-99
    • (1975) Math. Proc. Camb. Phil. Soc. , vol.77 , pp. 43-69
    • Atiyah, M.F.1    Patodi, V.K.2    Singer, I.M.3
  • 4
    • 0016578269 scopus 로고
    • M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry. I,II,III, Math. Proc. Camb. Phil. Soc. 77 (1975) 43-69; 78 (1975) 405-432; 79 (1976) 71-99
    • (1975) Math. Proc. Camb. Phil. Soc. , vol.78 , pp. 405-432
  • 5
    • 84923270175 scopus 로고
    • M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry. I,II,III, Math. Proc. Camb. Phil. Soc. 77 (1975) 43-69; 78 (1975) 405-432; 79 (1976) 71-99
    • (1976) Math. Proc. Camb. Phil. Soc. , vol.79 , pp. 71-99
  • 6
    • 84974000867 scopus 로고
    • Unitary representations of Brieskorn spheres
    • H U Boden, Unitary representations of Brieskorn spheres, Duke J. Math. 75 (1994) 193-220
    • (1994) Duke J. Math. , vol.75 , pp. 193-220
    • Boden, H.U.1
  • 7
    • 0032172101 scopus 로고    scopus 로고
    • The SU(3) Casson invariant for integral homology 3-spheres
    • H U Boden, C M Herald, The SU(3) Casson invariant for integral homology 3-spheres, J. Diff. Geom. 50 (1998) 147-206
    • (1998) J. Diff. Geom. , vol.50 , pp. 147-206
    • Boden, H.U.1    Herald, C.M.2
  • 9
    • 84972528417 scopus 로고
    • On the gluing problem for the η-invariant
    • U Bunke, On the gluing problem for the η-invariant, J. Diff. Geom. 41 (1995) 397-448
    • (1995) J. Diff. Geom. , vol.41 , pp. 397-448
    • Bunke, U.1
  • 10
    • 84967800145 scopus 로고
    • A symplectic geometry approach to generalized Casson's invariant
    • S Cappell, R Lee, E Miller, A symplectic geometry approach to generalized Casson's invariant, Bull. Amer. Math. Soc. 22 (1990) 269-275
    • (1990) Bull. Amer. Math. Soc. , vol.22 , pp. 269-275
    • Cappell, S.1    Lee, R.2    Miller, E.3
  • 12
    • 0030494290 scopus 로고    scopus 로고
    • Self-adjoint elliptic operators and manifold decompositions: I. Low eigenmodes and stretching
    • S Cappell, R Lee, E Miller Self-adjoint elliptic operators and manifold decompositions: I. Low eigenmodes and stretching, Comm. Pure Appl. Math. 49 (1996) 825-866; II. Spectral flow and Maslov index, 49 (1996) 869-909
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 825-866
    • Cappell, S.1    Lee, R.2    Miller, E.3
  • 13
    • 0030494290 scopus 로고    scopus 로고
    • S Cappell, R Lee, E Miller Self-adjoint elliptic operators and manifold decompositions: I. Low eigenmodes and stretching, Comm. Pure Appl. Math. 49 (1996) 825-866; II. Spectral flow and Maslov index, 49 (1996) 869-909
    • (1996) II. Spectral Flow and Maslov Index , vol.49 , pp. 869-909
  • 15
    • 22844453333 scopus 로고    scopus 로고
    • An extension of a theorem of Nicolaescu on spectral flow and the Maslov index
    • M Daniel, An extension of a theorem of Nicolaescu on spectral flow and the Maslov index, Proc. Amer. Math. Soc. 128 (2000) 611-619
    • (2000) Proc. Amer. Math. Soc. , vol.128 , pp. 611-619
    • Daniel, M.1
  • 17
    • 0013182826 scopus 로고    scopus 로고
    • A general splitting theorem for spectral flow, with an appendix by KP Wojciechowski
    • M Daniel, P Kirk, A general splitting theorem for spectral flow, with an appendix by KP Wojciechowski, Michigan Math. J. 46 (1999) 589-617
    • (1999) Michigan Math. J. , vol.46 , pp. 589-617
    • Daniel, M.1    Kirk, P.2
  • 18
    • 0040656037 scopus 로고    scopus 로고
    • Jumps of the eta-invariant. With an appendix by S Weinberger: Rationality of ρ-invariants
    • M Farber, J Levine, Jumps of the eta-invariant. With an appendix by S Weinberger: Rationality of ρ-invariants. Math. Zeit. 223 (1996) 197-246
    • (1996) Math. Zeit. , vol.223 , pp. 197-246
    • Farber, M.1    Levine, J.2
  • 19
    • 0010143005 scopus 로고
    • A local analytic splitting of the holonomy map on flat connections
    • B Fine, P Kirk, E Klassen, A local analytic splitting of the holonomy map on flat connections, Math. Ann. 299 (1994) 171-189
    • (1994) Math. Ann. , vol.299 , pp. 171-189
    • Fine, B.1    Kirk, P.2    Klassen, E.3
  • 20
    • 84960552822 scopus 로고
    • Instanton homology of Seifert-fibered 3-spheres
    • R Fintushel, R Stern, Instanton homology of Seifert-fibered 3-spheres, Proc. Lond. Math. Soc. (3) 61 (1990) 109-138
    • (1990) Proc. Lond. Math. Soc. , vol.61 , Issue.3 , pp. 109-138
    • Fintushel, R.1    Stern, R.2
  • 22
    • 0000669016 scopus 로고
    • Chern-Simons invariants of 3-manifolds and representation spaces of knot groups
    • P Kirk, E Klassen, Chern-Simons invariants of 3-manifolds and representation spaces of knot groups, Math. Ann. 287 (1990) 347-367
    • (1990) Math. Ann. , vol.287 , pp. 347-367
    • Kirk, P.1    Klassen, E.2
  • 23
    • 84972513561 scopus 로고
    • Computing spectral flow via cup products
    • P Kirk, E Klassen, Computing spectral flow via cup products, J. Diff. Geom. 40 (1994) 505-562
    • (1994) J. Diff. Geom. , vol.40 , pp. 505-562
    • Kirk, P.1    Klassen, E.2
  • 24
    • 0030295139 scopus 로고    scopus 로고
    • Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary
    • P Kirk, E Klassen, Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary, Mem. Amer. Math. Soc. 124 (1996) no. 592
    • (1996) Mem. Amer. Math. Soc. , vol.124 , Issue.592
    • Kirk, P.1    Klassen, E.2
  • 25
    • 21444439374 scopus 로고    scopus 로고
    • The spectral flow of the odd signature operator and higher Massey products
    • P Kirk, E Klassen, The spectral flow of the odd signature operator and higher Massey products, Math. Proc. Camb. Phil. Soc. 121 (1997) 297-320
    • (1997) Math. Proc. Camb. Phil. Soc. , vol.121 , pp. 297-320
    • Kirk, P.1    Klassen, E.2
  • 26
    • 0039401915 scopus 로고    scopus 로고
    • Continuity and analyticity of families of self-adjoint Dirac operators on a manifold with boundary
    • P Kirk, E Klassen, Continuity and analyticity of families of self-adjoint Dirac operators on a manifold with boundary, Illinois J. Math. 42 (1998) 123-138
    • (1998) Illinois J. Math. , vol.42 , pp. 123-138
    • Kirk, P.1    Klassen, E.2
  • 27
    • 51249166184 scopus 로고
    • Splitting the spectral flow and the Alexander matrix
    • P Kirk, E Klassen, D Ruberman, Splitting the spectral flow and the Alexander matrix, Comm. Math. Helv. 69 (1994) 375-416
    • (1994) Comm. Math. Helv. , vol.69 , pp. 375-416
    • Kirk, P.1    Klassen, E.2    Ruberman, D.3
  • 29
    • 84966232256 scopus 로고
    • Representations of knot groups in SU(2)
    • E Klassen, Representations of knot groups in SU(2), Trans. Amer. Math. Soc. 326 (1991) 795-828
    • (1991) Trans. Amer. Math. Soc. , vol.326 , pp. 795-828
    • Klassen, E.1
  • 30
    • 4344571234 scopus 로고    scopus 로고
    • Fermat limit and congruence of Ohtsuki invariants
    • Proceedings of the Kirbyfest (Berkeley, CA, 1998)
    • X-S Lin, Z Wang, Fermat limit and congruence of Ohtsuki invariants, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)", Geometry and Topology Monographs 2 (1999) 321-333
    • (1999) Geometry and Topology Monographs , vol.2 , pp. 321-333
    • Lin, X.-S.1    Wang, Z.2
  • 31
    • 4344695334 scopus 로고
    • private communication of unpublished research
    • T Mrowka, K Walker, private communication of unpublished research (1993)
    • (1993)
    • Mrowka, T.1    Walker, K.2
  • 32
    • 84973998973 scopus 로고
    • The Maslov index, the spectral flow, and splittings of manifolds
    • L Nicolaescu, The Maslov index, the spectral flow, and splittings of manifolds, Duke Math. J. 80 (1995) 485-533
    • (1995) Duke Math. J. , vol.80 , pp. 485-533
    • Nicolaescu, L.1
  • 33
    • 0031188080 scopus 로고    scopus 로고
    • Generalized symplectic geometries and the index of families of elliptic problems
    • L Nicolaescu, Generalized symplectic geometries and the index of families of elliptic problems, Mem. Amer. Math. Soc. 126 (1997) no. 609
    • (1997) Mem. Amer. Math. Soc. , vol.126 , Issue.609
    • Nicolaescu, L.1
  • 34
    • 84972521544 scopus 로고
    • Casson's invariant and gauge theory
    • C Taubes, Casson's invariant and gauge theory, J. Diff. Geom. 31 (1990) 547-599
    • (1990) J. Diff. Geom. , vol.31 , pp. 547-599
    • Taubes, C.1
  • 35
    • 0003332777 scopus 로고
    • An extension of Casson's invariant
    • Princeton University Press
    • K Walker, An extension of Casson's invariant, Annals of Math Studies 126, Princeton University Press (1992)
    • (1992) Annals of Math Studies , vol.126
    • Walker, K.1


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