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Book Categories |
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 |
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