English

Gromov's Oka principle, fiber bundles and the conformal module

Complex Variables 2023-12-20 v2

Abstract

The conformal module of conjugacy classes of braids is an invariant that appeared earlier than the entropy of conjugacy classes of braids, and is inverse proportional to the entropy. Using the relation between the two invariants we give a short conceptional proof of an earlier result on the conformal module. Mainly, we consider situations, when the conformal module of conjugacy classes of braids serves as obstruction for the existence of homotopies (or isotopies) of smooth objects involving braids to the respective holomorphic objects, and present theorems on the restricted validity of Gromov's Oka principle in these situations.

Keywords

Cite

@article{arxiv.2105.13938,
  title  = {Gromov's Oka principle, fiber bundles and the conformal module},
  author = {Burglind Jöricke},
  journal= {arXiv preprint arXiv:2105.13938},
  year   = {2023}
}

Comments

70 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1412.7000