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References
Abe, K.: On the tortal torsion and a generic property of closed regular curves in Riemannian manifolds, Preprint.
Alvarez-Gaumé, L.-Della Pietra, S.-Della Pietra, V.: The chiral determinant and the eta invariant, Commun. Math. Phys., 109 (1987), 691–700.
Andersson, S.I.: Non-Abelian Hodge theory via heat flow, Lect. Notes in Math., 1209 (1986), 8–36, Springer, Berlin.
Asada, A.: Flat connections of differential operators and odd dimensional characteristic classes, Jour. Fac. Sci. Shinshu Univ., 17 (1982), 1–30.
Asada, A.: Non Abelian de Rham theories, Topics in Differential Geometry, 83–115, North-Holland, Amsterdam, 1988.
Asada, A.: Non abelian Poincaré lemma, Lect. Notes in Math., 1209 (1986), 37–65, Springer, Berlin.
Asada, A.: Non Abelian de Rham theory, Prospects of Mathematical Science, 13–30, World Scientific, Singapore, 1988.
Asada,A.: Differential geometry of loop spaces, Loop gauge theory, and non abelian de Rham theory, Topological Aspects of Modern Physics, 176–208, Kyusyu Univ., 1988.
Asada, A.: Monodromy of a differential equation having a quadratic non linear term, Jour. Fac. Sci., Shinshu Univ., 22 (1987), 27–37.
Bismut, J.M.: Transgressed Chern forms for Dirac operators, Jour. Funct. Anal., 77 (1988), 32–50.
Brauer, R.: Sur les invariants intégraux des variétés représentatives des groupes de Lie simples clos, C. R. Sc. Paris, 202 (1935), 419–421, Coll. Papers, III, 443–445.
Chan, H.M.-Scharbach, P.-Tsou, S.T.: On loop space formulation of gauge theories, Ann. of Phys., 166 (1986), 396–421.
Della Pietra, S.-Della Pietra, V.: Parallel transport in the determinant line bundle, The zero index case, The non-zero index case, Commun. Math. Phys., 110 (1987), 573–599, 111 (1987), 11–31.
Gaveau, B.: Intégrales harmoniques non-abéliennes, Bull. Sc. Math., 2e série 106 (1982), 113–169.
Karoubi,M.: Cyclic homology and characteristic classes of bundles with additional structures, Preprint.
Killingback, T.P.: World-sheet anomalies and loop geometry, Nucl. Phys., B288 (1987), 578–588.
Lashof, R.: Classification of fibre bundles by the loop space of the base, Ann. Math., 64 (1956), 436–446.
Manin, Yu.I.: Gauge field and cohomology of analytic sheaves, Lect. Notes in Math., 970 (1982), 43–52, Springer, Berlin.
Mickelsson, J.-Rajeev, S.G.: Current algebra in d+1-Dimensions and determinant bundles over infinite-dimensional Grassmanians, Commun. Math. Phys., 116 (1988), 365–400.
Milnor, J.: Construction of universal bundles, I, Ann. Math., 63 (1956), 272–284.
Oniščik, A.L.: Some concepts and applications of non-Abelian cohomology theory, Trans. Moscow Math. Soc., 17 (1967), 49–98.
Pekonen, O.E.T.: Invariants secondaires de fibrés plants, C. R. Acad. Sc. Paris, 304 (1987), 13–14.
Pilch, K.-Warner, N.P.: String structures and the index of the Dirac-Ramond operator on orbifolds, Commun. Math. Phys., 115 (1988), 191–212.
Pressley,A.-Segal,G.: Loop Groups, Oxford, 1986.
Quillen, D.: Higher algebraic K-theory, I, Lect. Notes in Math., 341 (1973), 85–147, Springer, Berlin.
Röhrl, H.: Das Riemann-Hilbertsche Problem der Theorie der linearen Differentialgleichungen, Math. Ann., 133 (1957), 1–25.
Steenrod,N.E.: The Topology of Fibre Bundles, Princeton, 1951.
Vassiliou, E.: Total differential equations and the structure of fibre bundles, Bull. Greek Math. Soc., 27 (1986), 149–159.
Vourdas, A.: Loop gauge theory and group cohomology, Jour. Math. Phys., 28 (1987), 584–591.
Weil,A.: Fibre spaces in algebraic geometry, Univ. of Chicago, 1952.
Mensky,M.B.: Group of Paths, Observations, Fields, and Particles, Moscow, 1983 (in Russian), (Japanese translation, Sugano,K.: Keiro-Gun no Kikagaku to Soryusi-Ron, Yosioka Syoten, Tokyo, 1988).
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Asada, A. (1989). Integrable forms on iterated loop spaces and higher dimensional non abelian de Rham theory. In: Carreras, F.J., Gil-Medrano, O., Naveira, A.M. (eds) Differential Geometry. Lecture Notes in Mathematics, vol 1410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086409
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