Collected Papers of K.-T. Chen

ISBN-13: 9780817640057 / Angielski / Twarda / 2001 / 734 str.

K. -T Chen; P. Tondeur; Philippe Tondeur

Opis

Kuo-Tsai Chen (1923-1987) is best known to the mathematics community for his work on iterated integrals and power series connections in conjunction with his research on the cohomology of loop spaces. This text provides a comprehensive collection of Chen's mathematical publications.

Spis treści

[1] Integration in free groups.- [2] Commutator calculus and link invariants.- [3] Isotopy invariants of links.- [4] A group ring method for finitely generated groups.- [5] Iterated integrals and exponential homomorphisms.- [6] On the composition functions of nilpotent Lie groups.- [7] Integration of paths, geometric invariants and a generalized Baker—Hausdorff formula.- [8] Integration of paths, a faithful representation of paths by noncommutative formal power series.- [9] Exponential isomorphism for vector spaces and its connection with Lie groups.- [10] Free differential calculus IV.- [11] Linear independence of exponentials of Lie elements.- [12] Formal differential equations.- [12A] Formal differential equations.- [13] Decomposition of differential equations.- [13A] Decomposição de Equações Diferencias.- [14] An expansion formula for differential equations.- [15] Decomposition and equivalence of local vector fields.- [16] Expansion of solutions of differential systems.- [17] On local diffeomorphisms about an elementary fixed point.- [18] Equivalence and decomposition of vector fields about an elementary critical point.- [19] Local diffeomorphism—C? realization of formal properties.- [20] On a generalization of Picard’s approximation.- [21] On nonelementary hyperbolic fixed points of diffeomorphisms.- [22] Iterated path integrals and generalized paths.- [23] Algebraization of iterated integration along paths.- [24] Normal forms of local diffeomorphisms on the real line.- [25] Algebraic paths.- [26] Homotopy of algebras.- [27] Covering-space-like algebras.- [28] An algebraic dualization of fundamental groups.- [29] Exact dynamic systems are tree-like and vice versa.- [30] A sufficient condition for non-abelianness of fundamental groups of differentiable manifolds.- [31] Algebras of iterated path integrals and fundamental groups.- [32] Differential forms and homotopy groups.- [32A] Iterated integration and loopspace cohomology.- [33] On Whitehead products.- [34] Free subalgebras of loop space homology and Massey products.- [35] Iterated integrals of differential forms and loop space homology.- [36] Fundamental groups, nilmanifolds and iterated integrals.- [37] Solvability on manifolds by quadratures permitting only integrals.- [38] Connections, holonomy and path space homology.- [39] Iterated integrals, fundamental groups and covering spaces.- [40] Reduced bar constructions on de Rham complexes.- [41] Extension of C? function algebra by integrals and Malcev completion of ?1.- [42] Iterated path integrals.- [43] Pullback de Rham cohomology of the free path fibration.- [44] Path space differential forms and transports of connections.- [45] Circular bar construction.- [46] Poles of maps onto Pn(C) and Whitehead integrals.- [47] Pullback path fibrations, homotopies and iterated integrals.- [48] The Euler operator.- [49] On the Hopf index theorem and the Hopf invariant.- [50] Pairs of maps into complex projective space.- [50A] On differentiable spaces.- [51] Degeneracy indices and Chern classes.- [52] On the Bézout theorem.- [53] Loop spaces and differential forms.- [54] Smooth maps, pullback path spaces, connections, and torsions.