Iterated Integrals and Cycles on Algebraic Manifolds Book

1	Iterated integrals, Chen's flat connection and [pi][subscript 1]	1
1.1	Introduction	1
1.2	Differential equations	2
1.3	Program	7
1.4	Lie algebras	8
1.5	Chen's Lie algebra and connection	14
1.6	Some work of Quillen	19
1.7	Group homology	21
1.8	The basic isomorphisms	25
1.9	Lattices in nilpotent Lie groups	26
1.10	Some Hodge theory	28
2	Iterated integrals on compact Riemann surfaces	35
2.1	Introduction	35
2.2	Generalities on Riemann surfaces and iterated integrals	35
2.3	Harmonic volumes and iterated integrals	42
2.4	Use of the Jacobian	45
2.5	Variational formula for harmonic volume	47
2.6	Algebraic equivalence and homological equivalence of algebraic cycles	52
2.7	Calculations for the degree 4 Fermat curve	55
2.8	Currents and Hodge theory	67
3	The generalized linking pairing and the heat kernel	73
3.1	Introduction	73
3.2	The main theorem	84
App	Orientations, fiber integration	95