×

zbMATH — the first resource for mathematics

Algebras of iterated path integrals and fundamental groups. (English) Zbl 0217.47705

MSC:
53C65 Integral geometry
58A99 General theory of differentiable manifolds
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kuo-Tsai Chen, Iterated integrals and exponential homomorphisms, Proc. London Math. Soc. (3) 4 (1954), 502 – 512. · Zbl 0058.25603 · doi:10.1112/plms/s3-4.1.502 · doi.org
[2] Kuo-Tsai Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math. (2) 65 (1957), 163 – 178. · Zbl 0077.25301 · doi:10.2307/1969671 · doi.org
[3] Kuo-Tsai Chen, Integration of paths — a faithful representation of paths by non-commutative formal power series, Trans. Amer. Math. Soc. 89 (1958), 395 – 407. · Zbl 0097.25803
[4] Kuo-Tsai Chen, Exponential isomorphism for vector spaces and its connection with Lie groups, J. London Math. Soc. 33 (1958), 170 – 177. · Zbl 0083.02202 · doi:10.1112/jlms/s1-33.2.170 · doi.org
[5] Kuo-tsai Chen, Formal differential equations, Ann. of Math. (2) 73 (1961), 110 – 133. · Zbl 0098.05702 · doi:10.2307/1970284 · doi.org
[6] Kuo-tsai Chen, Iterated path integrals and generalized paths, Bull. Amer. Math. Soc. 73 (1967), 935 – 938. · Zbl 0179.19601
[7] Kuo-tsai Chen, Algebraic paths, J. Algebra 10 (1968), 8 – 36. · Zbl 0204.33803 · doi:10.1016/0021-8693(68)90102-6 · doi.org
[8] Kuo-tsai Chen, Homotopy of algebras, J. Algebra 10 (1968), 183 – 193. · Zbl 0167.03704 · doi:10.1016/0021-8693(68)90094-X · doi.org
[9] Kuo-tsai Chen, An algebraic dualization of fundamental groups, Bull. Amer. Math. Soc. 75 (1969), 1020 – 1024. · Zbl 0182.57101
[10] Kuo Tsai Chen, Covering-space-like algebras, J. Algebra 13 (1969), 308 – 326. · Zbl 0181.32501 · doi:10.1016/0021-8693(69)90077-5 · doi.org
[11] Kuo-tsai Chen, A sufficient condition for nonabelianness of fundamental groups of differentiable manifolds, Proc. Amer. Math. Soc. 26 (1970), 196 – 198. · Zbl 0197.49303
[12] H. H. Johnson, A generalization of K. T. Chen’s invariants for paths under transformation groups, Trans. Amer. Math. Soc. 105 (1962), 453 – 461. · Zbl 0124.14902
[13] David Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431 – 449. · Zbl 0146.19201
[14] W. S. Massey, Some higher order cohomology operations, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 145 – 154. · Zbl 0123.16103
[15] John W. Milnor and John C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211 – 264. · Zbl 0163.28202 · doi:10.2307/1970615 · doi.org
[16] A. N. Paršin, On a certain generalization of Jacobian manifold, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 175 – 182 (Russian).
[17] Rimhak Ree, Lie elements and an algebra associated with shuffles, Ann. of Math. (2) 68 (1958), 210 – 220. · Zbl 0083.25401 · doi:10.2307/1970243 · doi.org
[18] Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. · Zbl 0194.32901
[19] André Weil, Introduction à l’étude des variétés kählériennes, Publications de l’Institut de Mathématique de l’Université de Nancago, VI. Actualités Sci. Ind. no. 1267, Hermann, Paris, 1958 (French). · Zbl 0137.41103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.