Iterated Integrals and Homotopy Periods.
- 1st ed.
- 1 online resource (104 pages)
- Memoirs of the American Mathematical Society ; v.47 .
- Memoirs of the American Mathematical Society .
Intro -- CONTENTS -- 1. INTRODUCTION -- 2. HOW TO COMPUTE ∏[sub(*)](M) ࣯ R USING DIFFERENTIAL FORMS -- The Whitehead Product -- The de Rham Theorem -- Power Series Connections -- The Main Theorem -- Appendix -- 3. NOTATION AND CONVENTIONS -- 4. POWER SERIES CONNECTIONS ON SEMISIMPLICIAL COMPLEXES -- Differentiable Spaces -- Polynomial Forms on an s.s.c. -- Connections on Cochain Algebras -- The Main Theorem -- 5. ITERATED INTEGRALS -- Loop Spaces -- Iterated Integrals -- Properties of Iterated Integrals -- 6. POWER SERIES CONNECTIONS REVISITED -- The Smoothing Lemma -- Loop Space Cohomology -- The Transport of a Connection -- The Lie Transport -- Uniqueness and Naturality of Power Series Connections -- Topological Interpretation of the Model -- 7. ITERATED INTEGRALS AND H0M0T0PY PERIODS -- Iterated integrals and Minimal Models -- 8. A PROOF OF THE SMOOTHING LEMMA -- 9. PROOFS OF THE RATIONAL LOOP SPACE HOLOMOGY AND COHOMOLOGY THEOREMS -- REFERENCES.