Description
Book Synopsis1. Introduction.- 2. Riemann Surfaces, Braids, Mapping Classes, and Teichmueller Theory.- 3. The entropy of surface homeomorphisms.- 4. Conformal invariants of homotopy classes of curves. The Main theorem.- 5. Reducible pure braids. Irreducible nodal components, irreducible braid components, and the proof of the Main Theorem.- 6. The general case. Irreducible nodal components, irreducible braid components, and the proof of the Main Theorem.- 7. The conformal module and holomorphic families of polynomials.- 8. Gromov's Oka Principle and conformal module.- 9. Gromov's Oka Principle for (g, m)-fiber bundles.- 10. Fundamental groups and bounds for the extremal length.- 11. Counting functions.- 12. Riemann surfaces of second kind and finiteness theorems.- A. Several complex variables.- B. A Lemma on Conjugation.- C. Koebe's Theorem.- Index.- References.
