2026-07-19T17:49:50Zhttps://ce.visuallibrary.net/ubpb/oai/

oai:ce.visuallibrary.net/ubpb:13338242025-04-17T15:01:01Zubpbcebook

vls/2603nrwcece.visuallibrary.netvdBraids, conformal module, entropy, and Gromov's Oka PrincipleJöricke, BurglindVerfasserauttextTextbookszXA-CHCham, SwitzerlandSpringer[2025]© 20252025monographicengprintxv, 426 Seiten Illustrationen, Diagrammeohne Hilfsmittel zu benutzenBandThis book studies the relation between conformal invariants and dynamical invariants and their applications, taking the reader on an excursion through a wide range of topics. The conformal invariants, called here the conformal modules of conjugacy classes of elements of the fundamental group, were proposed by Gromov in the case of the twice punctured complex plane. They provide obstructions to Gromov's Oka Principle. The invariants of the space of monic polynomials of degree n appeared earlier in relation to Hilbert's 13th Problem, and are called the conformal modules of conjugacy classes of braids. Interestingly, the conformal module of a conjugacy class of braids is inversely proportional to a popular dynamical invariant, the entropy, which was studied in connection with Thurston's celebrated theory of surface homeomorphisms. This result, proved here for the first time, is another instance of the numerous manifestations of the unity of mathematics, and it has applications. After prerequisites on Riemann surfaces, braids, mapping classes and elements of Teichmüller theory, a detailed introduction to the entropy of braids and mapping classes is given, with thorough, sometimes new proofs. Estimates are provided of Gromov's conformal invariants of the twice punctured complex plane and it is shown that the upper and lower bounds differ by universal multiplicative constants. These imply estimates of the entropy of any pure three-braid, and yield quantitative statements on the limitations of Gromov's Oka Principle in the sense of finiteness theorems, using conformal invariants which are related to elements of the fundamental group (not merely to conjugacy classes). Further applications of the concept of conformal module are discussed. Aimed at graduate students and researchers, the book proposes several research problems.Burglind JörickeFunctions of complex variables.Dynamical systems.Algebraic geometry.Manifolds (Mathematics).515.94SI 850978303167287399375315435706441HT030951850Online-Ausgabe9783031672880Lecture notes in mathematics2360(DE-605)HT001253222rda25021820250414120836.02561643ger https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D2561643 https://ce.visuallibrary.net/id/1333824 https://ce.visuallibrary.net/i3f/v20/1333824/manifest https://ce.visuallibrary.net/proto_ftsearch/1333824