Description

Book Synopsis

1. 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.

Braids Conformal Module Entropy and Gromovs Oka

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      Book details

      Publisher Springer
      Published 3 October 2025
      ISBN-13 9783031672873
      978-3031672873
      ISBN-10 3031672879
      Also in:
      Mathematics Complex analysis, complex variables

      Description

      Book Synopsis

      1. 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.

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