The geometry of loop groups
Daniel S. Freed
Source: J. Differential Geom. Volume 28, Number 2
(1988), 223-276.
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Zentralblatt MATH identifier: 0619.58003
References
[1] W. Ambrose and I. M. Singer, A theorem on holonomy, Trans. Amer. Math. Soc. 75 (1953) 428-443.
Zentralblatt MATH: 0052.18002
Mathematical Reviews (MathSciNet): MR63739
Digital Object Identifier: doi:10.2307/1990721
[2] D. W. Andersen and L. Hodgkin, The K-theory of Eilenberg-Mac Lane complexes, Topology 1 (1968) 371-329.
Zentralblatt MATH: 0199.26302
[3] M. F. Atiyah, Algebraic topology and operators in Hilbert space, Lecture Notes in Math., Vol. 103, Springer, New York, 1969, 101-121.
Zentralblatt MATH: 0177.51701
Mathematical Reviews (MathSciNet): MR248803
Digital Object Identifier: doi:10.1007/BFb0099987
[4] M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982) 1-15.
Zentralblatt MATH: 0482.58013
Mathematical Reviews (MathSciNet): MR642416
Digital Object Identifier: doi:10.1112/blms/14.1.1
[5] M. F. Atiyah, Instantons in two and four dimensions, Comm. Math. Phys. 93 (1984) 437-451.
Zentralblatt MATH: 0564.58040
Mathematical Reviews (MathSciNet): MR763752
Digital Object Identifier: doi:10.1007/BF01212288
Project Euclid: euclid.cmp/1103941176
[6] M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., Vol. 3, Amer. Math. Soc, Providence, RI, 1961.
Zentralblatt MATH: 0108.17705
Mathematical Reviews (MathSciNet): MR139181
[7] M. F. Atiyah, N. Hitchin and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London A 362 (1978) 425-461.
Zentralblatt MATH: 0389.53011
Mathematical Reviews (MathSciNet): MR506229
Digital Object Identifier: doi:10.1098/rspa.1978.0143
[8] M. F. Atiyah and W. Schmid, A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 42 (1977) 1-62.
Zentralblatt MATH: 0373.22001
Mathematical Reviews (MathSciNet): MR463358
Digital Object Identifier: doi:10.1007/BF01389783
[9] A. Borel, Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groups de Lie compacts, Ann. of Math. (2) 57 (1953) 115-207.
Zentralblatt MATH: 0052.40001
Mathematical Reviews (MathSciNet): MR51508
Digital Object Identifier: doi:10.2307/1969728
JSTOR: links.jstor.org
[10] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, Part I, Amer. J. Math. 80 (1958) 438-538.
Zentralblatt MATH: 0097.36401
Mathematical Reviews (MathSciNet): MR102800
Digital Object Identifier: doi:10.2307/2372795
JSTOR: links.jstor.org
[11] R. Bott, An application of the Morse theory to the topology of Lie groups, Bull. Soc. Math. France 84 (1956) 251-281.
Zentralblatt MATH: 0073.40001
Mathematical Reviews (MathSciNet): MR87035
[12] R. Bott, The space of loops on a Lie group, Michigan Math. J. 5 (1958) 35-61.
Zentralblatt MATH: 0096.17701
Mathematical Reviews (MathSciNet): MR102803
Digital Object Identifier: doi:10.1307/mmj/1028998010
Project Euclid: euclid.mmj/1028998010
[13] R. Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959) 313-337.
Zentralblatt MATH: 0129.15601
Mathematical Reviews (MathSciNet): MR110104
Digital Object Identifier: doi:10.2307/1970106
JSTOR: links.jstor.org
[14] R. Bott and H. Samelson, Application of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958) 964-1029.
Zentralblatt MATH: 0101.39702
Mathematical Reviews (MathSciNet): MR105694
Digital Object Identifier: doi:10.2307/2372843
JSTOR: links.jstor.org
[15] M. J. Bowick and S. G. Rajeev, String Theory as the Kahler geometry of loop spaces, preprint.
[16] S. K. Donaldson, Instantons and geometric invariant theory, Comm. Math. Phys. 93 (1984) 453-60.
Zentralblatt MATH: 0581.14008
Mathematical Reviews (MathSciNet): MR763753
Digital Object Identifier: doi:10.1007/BF01212289
Project Euclid: euclid.cmp/1103941177
[17] J. Eells, Jr., A setting for global analysis, Bull. Amer. Math. Soc. 72 (1966) 751-807.
Zentralblatt MATH: 0191.44101
Mathematical Reviews (MathSciNet): MR203742
Digital Object Identifier: doi:10.1090/S0002-9904-1966-11558-6
Project Euclid: euclid.bams/1183528314
[18] K. D. Elworthy and A. J. Tromba, Differential structures and Fredholm maps on Banach manifolds, Proc. Sympos. Pure Math., Vol. 15, Amer. Math. Soc, Providence, RI, 1970, 45-94.
Zentralblatt MATH: 0206.52504
Mathematical Reviews (MathSciNet): MR264708
[19] D. S. Freed, Flag manifolds and infinite dimensional Kahler geometry, in Infinite Dimensional Lie Groups (V. G. Kac, ed.), Math. Sci. Res. Inst. Publ., Vol. 4, Springer, New York, 1985.
Zentralblatt MATH: 0595.22016
Mathematical Reviews (MathSciNet): MR823316
[20] D. S. Freed, An index theorem for families of Fredholm operators parametrized by a group, Topology, to appear.
Zentralblatt MATH: 0673.58004
Mathematical Reviews (MathSciNet): MR963631
Digital Object Identifier: doi:10.1016/0040-9383(88)90010-9
[21] D. S. Freed and D. Groisser, The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group, preprint.
Zentralblatt MATH: 0694.58008
Mathematical Reviews (MathSciNet): MR1027070
Digital Object Identifier: doi:10.1307/mmj/1029004004
Project Euclid: euclid.mmj/1029004004
[22] D. S. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, Math. Sci. Res. Inst. Publ., Vol. 1, Springer, New York, 1984.
Zentralblatt MATH: 0559.57001
Mathematical Reviews (MathSciNet): MR757358
[23] J. W. Helton and R. E. Howe, Integral operators: traces, index, and homology, in Proceedings of a Conference on Operator Theory, Lecture Notes in Math., Vol. 345, Springer, New York, 1973, 141-209.
Zentralblatt MATH: 0268.47054
Mathematical Reviews (MathSciNet): MR390829
[24] V. G. Kac, Infinite dimensional Lie algebras, Birkhauser, Boston, 1983.
Zentralblatt MATH: 0537.17001
Mathematical Reviews (MathSciNet): MR739850
[25] S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 2, Wiley-Interscience, New York, 1969.
Zentralblatt MATH: 0175.48504
[26] N. H. Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965) 19-30.
Zentralblatt MATH: 0129.38901
Mathematical Reviews (MathSciNet): MR179792
Digital Object Identifier: doi:10.1016/0040-9383(65)90067-4
[27] S. Lang, Differential manifolds, Addison-Wesley, Reading, MA., 1972.
Zentralblatt MATH: 0239.58001
Mathematical Reviews (MathSciNet): MR431240
[28] R. S. Palais, Foundations of global non-linear analysis, Benjamin, New York, 1968.
Zentralblatt MATH: 0164.11102
Mathematical Reviews (MathSciNet): MR248880
[29] R. S. Palais, Banach manifolds of fiber bundle sections, Actes Congres Internat. Math., Tome 2, 1970, 243-249.
Zentralblatt MATH: 0326.58008
Mathematical Reviews (MathSciNet): MR448405
[30] J. P. Penot, Sur le theoreme de Frobenius, Bull. Soc. Math. France 98 (1970) 47-80.
Zentralblatt MATH: 0197.41601
Mathematical Reviews (MathSciNet): MR266254
[31] A. N. Pressley, The energy flow on the loop space of a compact Lie group, J. London Math. Soc. (2)2 (1982) 557-566.
Zentralblatt MATH: 0508.58011
Mathematical Reviews (MathSciNet): MR684568
Digital Object Identifier: doi:10.1112/jlms/s2-26.3.557
[32] A. N. Pressley and G. B. Segal, Loop groups, Oxford University Press.
Zentralblatt MATH: 0618.22011
[33] R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure. Math., Vol. 10, Amer. Math. Soc, 1967, 288-307.
Zentralblatt MATH: 0159.15504
Mathematical Reviews (MathSciNet): MR237943
[34] G. B. Segal, Unitary representation of some infinite dimensional groups, Comm. Math. Phys. 80 (1981) 301-342.
Zentralblatt MATH: 0495.22017
Mathematical Reviews (MathSciNet): MR626704
Digital Object Identifier: doi:10.1007/BF01208274
Project Euclid: euclid.cmp/1103919978
[35] G. B. Segal, Faddeev's anomaly in Gauss' law, preprint.
Journal of Differential Geometry
