AffiliationMathematics Department, University of Arizona
MetadataShow full item record
PublisherOxford University Press (OUP)
CitationDalthorp, M., & Pickrell, D. (2021). Homeomorphisms of S1 and Factorization. International Mathematics Research Notices, 2021(22), 16859–16909.
Rights© The Author(s) 2019. Published by Oxford University Press. All rights reserved.
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AbstractFor each n>0 there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations "conjugated by z \to zn. We show that these families are free of relations, which determines the structure of "the group of homeomorphisms of finite type". We next consider factorization for more robust groups of homeomorphisms. We refer to this as root subgroup factorization (because the factors correspond to root subgroups). We are especially interested in how root subgroup factorization is related to triangular factorization (i.e., conformal welding) and correspondences between smoothness properties of the homeomorphisms and decay properties of the root subgroup parameters. This leads to interesting comparisons with Fourier series and the theory of Verblunsky coefficients.
Note12 month embargo; published: 04 December 2019
VersionFinal accepted manuscript